CN114154275B - Low-pressure turbine blade profile pneumatic design method based on optimal load distribution model optimization - Google Patents

Low-pressure turbine blade profile pneumatic design method based on optimal load distribution model optimization Download PDF

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CN114154275B
CN114154275B CN202210123438.3A CN202210123438A CN114154275B CN 114154275 B CN114154275 B CN 114154275B CN 202210123438 A CN202210123438 A CN 202210123438A CN 114154275 B CN114154275 B CN 114154275B
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刘子钰
陈俊锋
姚李超
轩笠铭
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Beihang University
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Abstract

The invention discloses a low-pressure turbine blade profile pneumatic design method based on optimal load distribution model optimization, which comprises the steps of generating a blade profile geometric sample according to a given blade profile parameter value range and low-dimensional pneumatic design parameters, calculating optimal load distribution when the total pressure loss of a blade profile is minimum through CFD, and generating a blade profile database; constructing an optimal load distribution model based on a multi-output Gaussian process and a deep neural network, and training the optimal load distribution model through a minimized marginal likelihood loss function according to training samples in a leaf database to obtain a super parameter set in the optimal load distribution model; and calculating the target optimal load distribution of the target low-dimensional pneumatic design parameters according to the trained optimal load distribution model, and calculating the optimal pneumatic blade profile corresponding to the target optimal load distribution by using the blade profile inverse design model. The design method can improve the precision and efficiency of the turbine blade profile pneumatic design and shorten the geometric design period of the turbine blade profile.

Description

Low-pressure turbine blade profile pneumatic design method based on optimal load distribution model optimization
Technical Field
The invention relates to the technical field of turbine blade profile design, in particular to a low-pressure turbine blade profile pneumatic design method based on optimal load distribution model optimization.
Background
The turbine is a key part of an aircraft engine, is an impeller mechanical device for converting the energy of high-temperature and high-pressure gas into kinetic energy and mechanical energy, and the pneumatic performance of the part of the turbine has very important influence on the overall pneumatic performance, economy and environmental protection of the engine.
The turbine aerodynamic design usually faces complex design requirements, the aerodynamic performance is very sensitive to geometric changes, and a plurality of design requirements and geometric variables are coupled together to form a high-dimensional design space, so that a corresponding global optimal solution is difficult to obtain through theoretical quantitative analysis.
The conventional pneumatic design method generally requires high-precision CFD iterative computation, for example, in patent application with publication number CN112380794A, the design method disclosed in the invention is a multidisciplinary parallel collaborative optimization design method for blades of an aircraft turbine engine, and the design method is high in computation cost and long in design period, and most of the design methods are optimized based on a gradient method, so that the design method is easy to fall into a local minimum value.
Although a proxy model based on neural network or gaussian process regression can be utilized to reduce the time consumption of CFD calculation, the computational accuracy of such a proxy model is relatively poor, and as design variables in the proxy model gradually increase, such a proxy model algorithm faces a serious dimension disaster problem, which results in that it cannot establish a general proxy model between a wide range of design conditions and leaf geometry and aerodynamic performance.
Disclosure of Invention
The invention aims to: how to establish a mapping relation between low-dimensional pneumatic design parameters and optimal load distribution when total pressure loss is minimum in the process of designing the turbine blade geometry so as to improve the precision and efficiency of the turbine blade pneumatic design and shorten the design period of the turbine blade geometry.
The technical scheme of the invention is as follows:
a low-pressure turbine blade profile aerodynamic design method based on optimal load distribution model optimization comprises the following steps:
step 1, generating a leaf profile geometric sample B according to a given leaf profile parameter value range and low-dimensional pneumatic design parameters, calculating optimal load distribution when the total pressure loss of the leaf profile is minimum through CFD, and generating a leaf profile database;
step 2, based onConstructing an optimal load distribution model according to a multi-output Gaussian process and a deep neural network, training the optimal load distribution model through a minimized marginal likelihood loss function according to training samples in a leaf database to obtain a super parameter set in the optimal load distribution model, wherein the super parameter set is used for determining the trained optimal load distribution model, the optimal load distribution model is composed of a plurality of layers of neurons, and kernel functions of the neuronsK γ Comprises the following steps:
Figure 84696DEST_PATH_IMAGE001
in the formula (I), the compound is shown in the specification,g(x,w) In order to be an intermediate feature,wthe neural network weight parameter for the optimal load distribution model,r=|x-x' is two groups of random variablesxAndxthe distance of (a) to (b),K f is a semi-positive definite matrix and is provided with a positive definite matrix,θis a kernel functionK γ Is determined by the parameter (c) of (c),r(. cndot.) is a function of distance,
Figure 424542DEST_PATH_IMAGE002
to be the distance average of the training samples,nis a first preset parameter, and is a second preset parameter,n=1,2,…,5，mis the second preset parameter, and is the second preset parameter,m=2 or 3, the super parameter group includes at least weight parameterwHyper-parameterθAnd a semi-positive definite matrixK f ；
And 3, calculating the target optimal load distribution of the target low-dimensional pneumatic design parameters according to the trained optimal load distribution model, and calculating the optimal pneumatic blade profile corresponding to the target optimal load distribution by using a blade profile inverse design model.
Further, the step 1 specifically includes:
step 1.1, generating an initial blade profile parameter group P and a blade profile geometric sample B by utilizing a sampling function and a blade profile parameterization method in a given blade profile parameter value range according to low-dimensional pneumatic design parameters;
step 1.2, taking the low-dimensional pneumatic design parameters as boundary conditions, and carrying out CFD calculation on the leaf-shaped geometric sample B according to the initial leaf-shaped parameter group P to obtain the load distribution and the leaf-shaped total pressure loss corresponding to the leaf-shaped geometric sample B;
and 1.3, generating a blade parameter group P by using Bayes optimization iteration, and re-executing the step 1.1 until the load distribution with the minimum total pressure loss of the blade is obtained and recorded as the optimal load distribution.
Further, step S1.3 specifically includes:
step S1.3.1, establishing a Gaussian process model of the blade profile parameter group P and the blade profile total pressure loss, training the Gaussian process model by using the training sample set M, and updating the hyperparameter in the Gaussian process model;
and S1.3.2, based on the trained Gaussian process model, in a given leaf profile parameter value range, optimizing and selecting a leaf profile parameter group P by using a sampling function, re-executing the step 1.1, calculating load distribution and leaf profile total pressure loss corresponding to the leaf profile parameter group P, and updating the training sample set M until the optimal load distribution when the leaf profile total pressure loss is minimum is obtained.
Further, in the step 2, training the optimal load distribution model by minimizing a marginal likelihood loss function according to the training samples in the leaf database specifically includes:
step 2.1, constructing a marginal likelihood loss function containing a super parameter group according to the optimal load distribution model, wherein the calculation formula of the marginal likelihood loss function is as follows:
Figure 31104DEST_PATH_IMAGE003
in the formula (I), the compound is shown in the specification,pin order to be a marginal probability,γin order to be able to set the super-parameter,xfor the input random variables of the optimal load distribution model,yfor the output random variables of the optimal load distribution model,σis the variance of the noise and is,Iis a function of a kernelK γ Identity matrix with same dimension.
Step 2.2, respectively calculating the marginal likelihood loss function to the optimal loadWeight parameters of cloth modelwSemi-positive definite matrixK f And hyperparametersθPartial derivatives of (d);
and 2.3, setting a learning rate, and updating the super parameter group in the optimal load distribution model by adopting a gradient descent method so as to train the optimal load distribution model.
Compared with the prior art, the invention has the following beneficial effects:
according to the technical scheme, a conventional design database is utilized, based on a deep neural network and a multi-output Gaussian process, a kernel function of a neuron in an optimal load distribution model is optimized, and a mapping relation between low-dimensional pneumatic design parameters and optimal load distribution with minimum total pressure loss is established, so that the design requirement of the given low-dimensional pneumatic design parameters is met, the optimal pneumatic blade profile corresponding to the optimal load distribution form is directly predicted, the precision and the efficiency of pneumatic design of the turbine blade profile are improved, and the design period of the turbine blade profile is shortened. The concrete expression is as follows:
1. the aerodynamic design efficiency of the two-dimensional blade profile of the turbine is improved, the optimal aerodynamic blade profile with the optimal aerodynamic performance under the given low-dimensional aerodynamic design parameters is output within 1 second, and compared with a design method which needs hours or even days, the design period of the aerodynamic blade profile is greatly shortened;
2. the accumulated database is utilized, so that the pneumatic performance of the two-dimensional blade profile of the turbine is improved, and the economy of turbine parts is improved;
3. according to the invention, low-dimensional pneumatic design parameters and optimal load distribution are respectively used as the input and the output of the model, so that a proxy model with extremely high dimensionality, pneumatic design parameters, blade geometry and pneumatic performance is prevented from being directly constructed, the dimension reduction of a design variable space is realized, and the method has strong expansibility and universality;
4. with the continuous accumulation of the database, the technical scheme of the invention can be automatically expanded, the design level is continuously improved, and the experience dependence on pneumatic design experts can be reduced, thereby reducing the time and economic cost for cultivating high-level designers.
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The advantages of the above and/or additional aspects of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a diagram illustrating a mapping model of low dimensional design parameters and optimal load distribution in the method according to an embodiment of the present invention;
FIG. 2 is a graph of a comparison of the profile geometry to a Pak-B reference profile according to one embodiment of the present invention;
FIG. 3 is a graph of optimal load distribution versus Pak-B reference profile load distribution according to one embodiment of the present invention;
FIG. 4 is a schematic representation of a leaf-type inverse design model according to an embodiment of the present invention;
FIG. 5a is a simulated comparison graph of total pressure loss of a profile according to an embodiment of the invention;
FIG. 5b is a comparison of a leaf simulation according to one embodiment of the present invention;
FIG. 6 is a graph comparing angle of attack characteristics with a Pak-B reference profile, according to an embodiment of the present invention;
FIG. 7 is a graph comparing total pressure loss at different Reynolds numbers with a Pak-B reference profile, according to one embodiment of the invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments of the present invention and features of the embodiments may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited by the specific embodiments disclosed below.
As shown in fig. 1, the present embodiment provides a low-pressure turbine blade aerodynamic design method based on optimal load distribution model optimization, which includes:
step 1, according to the given leafGenerating a leaf-shaped geometric sample by the shape parameter value range and the low-dimensional pneumatic design parametersBAnd calculating the optimal load distribution when the total pressure loss of the blade profile is minimum through CFD to generate a blade profile database, wherein the blade profile database comprises low-dimensional pneumatic design parametersAOptimal load distributionC * Load distributionCAnd leaf geometry samplesB；
Specifically, the low dimensional aerodynamic design parameter in this implementation is defined by Mach numberMaReynolds numberReThe parameters are combined, and the corresponding database is as follows:
Figure 460686DEST_PATH_IMAGE004
in the formula (I), the compound is shown in the specification,Ais composed ofnA set of low-dimensional pneumatic design parameters is set,Ma i is as followsiThe number of the mach numbers of the groups,Re i is as followsiThe number of the reynolds of the group,Zw i is as followsiThe set characterizes the Zweifel coefficients of the load size,α i is as followsiThe air flow angle at the inlet of the stack,β i is as followsiA stack outlet airflow angle, wherein,nset of low dimensional pneumatic design parametersAMay be calculated based on the definitions of mach number and reynolds number in fluid mechanics. The inlet and outlet boundary conditions required by CFD calculation include the total inlet temperature parameterTTotal pressure at inletPOutlet back pressureP out And the like.
It should be noted that the low-dimensional pneumatic design parameters are dimensionless parameters, which ensures the universality of the whole model.
In this embodiment, the setting can be madenFor 1600 sets, the design space for the low-dimensional pneumatic design parameters is: mach number of 0.4 to 0.7, Reynolds number of 1.00X 104To 2.00X 105The Zweifel coefficient is 0.8 to 1.2, the inlet airflow angle is 10 degrees to 40 degrees, the outlet airflow angle is-65 degrees to-50 degrees, and the inlet airflow angle and the outlet airflow angle adopt axial included angles. Sampling is carried out in the design space by adopting an optimized Latin hypercube sampling method so as to uniformly cover the combination range of the aerodynamic parameters of the low-pressure turbineAnd (5) enclosing.
The step 1 specifically comprises the following steps:
step 1.1, generating an initial blade profile parameter set by utilizing a sampling function and a blade profile parameterization method in a given blade profile parameter value range according to low-dimensional pneumatic design parametersPAnd leaf geometry samplesBWherein, geometric samples of the profileBIncluding a plurality of blade profile geometries, a first blade profile geometry being associated with an initial set of blade profile parametersPCorresponds to an initial set of blade profile parameters, the initial set of blade profile parametersP13 parameters representing the leaf profile in a parameterization method;
specifically, this embodiment is mainly based on the Pritchard leaf-shape parameterization method and the bezier curve modeling method, and utilizes the sampling function to select a set of leaf-shape parameters within a given leaf-shape parameter value range, and combines the inlet-outlet airflow angle and the Zweifel coefficient defined by the low-dimensional pneumatic design parameters to generate a leaf-shape parameter set corresponding to the geometric initial leaf-shape geometryP。
The blade profile geometry defined by the parameterization method is shown in fig. 2, the curve above the blade profile geometry is the suction surface, the curve below the blade profile is the pressure surface, points 3 and 4 are the end points of the arc of the leading edge of the blade, points 1 and 5 are the end points of the arc of the trailing edge, and point 2 is the intersection point of the throat and the suction surface.
In this embodiment, the initial set of blade parametersPA total of 13 parameters are included as shown in table 1.
TABLE 1
(symbol) Means of Minimum value Maximum value
εle,ss(°) Leading edge suction surface wedge angle 10 20
εle,ps(°) Leading edge pressure face wedge angle 10 20
rle(mm) Radius of leading edge 1.5 2.5
ζ(°) Bending angle of tail edge 6 20
εte,ss(°) Wedge angle of trailing edge suction surface 3 18
εle,ps(°) Wedge angle of trailing edge pressure face 0 3
rte(mm) Radius of trailing edge 0.8 1
β0(°) Mounting angle 12 50
Cx Axial chord length -
α Inlet air flow angle - -
β Outlet air flow angle - -
S Grid pitch - -
t Length of throat - -
Wherein the content of the first and second substances,C x 、α、β、Sandtthese 5 parameters are composed of low-dimensional design parametersAAnd (6) determining. Axial chord lengthC x Can be set to a fixed value and can be set to,α、βgrid pitch consistent with parameters in a low-dimensional design parameter setSAnd throat lengthtIs calculated by the formula：
Figure 152698DEST_PATH_IMAGE005
Figure 827393DEST_PATH_IMAGE006
According to the 13 parameters, the Bezier curve can be used to obtain all coordinate points of the leaf profile.
In the present embodiment, the mode of generating the blade profile geometry is not limited, and the blade profile may be parameterized, or may be a mean camber line thickness distribution method, a Nurbs curve method, or the like.
Step 1.2, taking the low-dimensional pneumatic design parameters as boundary conditions, and according to the initial blade profile parameter groupPFor geometric sample of leaf profileBPerforming CFD calculation to obtain a leaf profile geometric sampleBCorresponding load distribution and total pressure loss of the blade profile.
In particular, in the low-dimensional pneumatic design parametersAAnd under the boundary conditions of the determined inlet total temperature, inlet total pressure, inlet airflow angle and outlet back pressure, CFD is adopted to calculate the generated blade profile geometric sample in the processBPerforming numerical simulation, and calculating load distribution and total pressure loss of each blade profile corresponding to each blade profile coordinate point, wherein the load distribution adopts a pressure coefficientC p Expressed, the corresponding calculation formula is:
Figure 554041DEST_PATH_IMAGE007
in the formula (I), the compound is shown in the specification,P tin the average total pressure at the inlet is,P in the average static pressure at the inlet is,Pis the blade profile surface static pressure.
The total pressure loss of the blade profile is used for representing the aerodynamic performance of the blade cascade, and the corresponding calculation formula is as follows:
Figure 420103DEST_PATH_IMAGE008
in the formula (I), the compound is shown in the specification,P tout the average total pressure at the outlet is,P out the average static pressure at the outlet is,Lossthe total pressure loss of the blade profile is shown.
It should be noted that, in this embodiment, the CFD numerical simulation is completed by using ANSYS CFX software, the inlet is given total temperature, total pressure, and spanwise distribution of the flow angle in the calculation, the outlet is given static pressure average value, the numerical simulation uses a multiple-mesh technique to accelerate convergence, and each blade channel adopts HO mesh topology.
Step 1.3, utilizing Bayesian optimization iteration to generate the set of leaf parameterPAnd re-executing the step 1.1 until obtaining the load distribution with the minimum total pressure loss of the blade profile, and recording the load distribution as the optimal load distribution, wherein the step 1.3 specifically comprises the following steps:
step 1.3.1, set of blade profile parametersPAs input, total pressure loss of the profileLossAs an output, a set of leaf profile parameters is establishedPAnd a Gaussian process model of total pressure loss of the leaf profile and utilizing a training sample setMAnd training the established Gaussian process model, and updating the hyper-parameters in the Gaussian process model so that the model has high prediction precision.
In particular, due to geometric sampling of the profileBIncluding a plurality of blade profile geometries, each blade profile geometry and blade profile parameter setPEach group of blade profile parameters corresponds to the total pressure loss of the corresponding blade profile through CFD calculation, and the second step is thattAt the time of secondary iteration, the leaf parameter set is utilizedPAnd the total pressure loss of the blade profile forms a training sample setM：
Figure 537095DEST_PATH_IMAGE009
Leaf profile parameter setPAs input, total pressure loss of the profileLossAs output, the following gaussian process model was established:
Figure 749902DEST_PATH_IMAGE010
in the formula (I), the compound is shown in the specification,E[·]in order to be a function of the expectation,f(x) As an input quantityxThe corresponding output quantity is output according to the output quantity,kin the form of a gaussian kernel function,GP(. cndot.) is a Gaussian process function.
Setting input quantity
Figure 829591DEST_PATH_IMAGE011
The stable nucleus isτ=|x-x' |, i.e. the distance between two different inputs, Gaussian kernel functionkIs a pair ofQThe kernel function obtained by the spectral density (Fourier transform) operation of the mixed gaussians corresponds to the calculation formula:
Figure 102440DEST_PATH_IMAGE012
Figure 769045DEST_PATH_IMAGE013
in the formula (I), the compound is shown in the specification,
Figure 519964DEST_PATH_IMAGE014
is as followsqA first mixed GausspThe covariance of the dimensions of the images,
Figure 719738DEST_PATH_IMAGE015
is as followsqA first mixed GausspThe mean value of the dimensions of the object,x p first of input quantitypThe number of the dimension elements is more than one,w q is shown asqThe weight of each mixture gaussian.
In updating the hyper-parameters in the Gaussian process model, in the first placetIn the secondary iteration process, setting the current training sample setMComprises the following steps:
Figure 429068DEST_PATH_IMAGE016
kernel in gaussian process modelThe hyper-parameter of the function is initialized to the first valuetHyper-parameters after 1 iterationθ t-1Training update superparameters by maximizing likelihood functions of Gaussian processesθ t-1Is composed ofθ t Wherein, the likelihood function calculation formula is:
Figure 317390DEST_PATH_IMAGE017
in the formula (I), the compound is shown in the specification,pto marginal probability, i.e.γ，xUnder known conditionsyMarginal probability at the gaussian process model;γin order to be able to set the super-parameter,γ={w,θ,K f }；xinputting a random variable;yis an output random variable;σis the variance of the noise;Iis a function of a kernelK γ Identity matrix with same dimension.
The updating process of the gaussian process model is as follows. Firstly, calculating the hyperparameter of the last iteration of the likelihood function pairθ t-1Partial derivatives of (a) and then artificially given learning ratesαUpdating the hyper-parameters by a gradient descent methodθ t The corresponding calculation formula is:
Figure 137578DEST_PATH_IMAGE018
utilizing updated hyper-parametersθ t Recalculating the likelihood function, continuously updating the hyperparameter until the likelihood function converges, at which time the corresponding hyperparameterθI.e. the hyper-parameters after the gaussian process model training. Note that the learning rateαCan be automatically adjusted by the Adam algorithm, and the Adam algorithm needs to add momentum correction in the gradient update.
Step 1.3.2, based on the trained Gaussian process model, in the given value range of the leaf parameter, optimizing and selecting a leaf parameter group by using a sampling functionPStep 1.1 is executed again to calculate the blade parameter setPCorresponding load distribution and total pressure of blade profileLoss, update training sample setMAnd obtaining the optimal load distribution when the total pressure loss of the blade profile is minimum.
Specifically, an Upper Confidence Bound (UCB) sampling function is used for the trained Gaussian process model to calculate any given initial leaf-shaped parameterx 0Function value of (c)f(x 0) Derivatives ofg 0', Hessian matrix of second derivativeH 0。
Thereafter, the next set of iteration points is determined by Newton's methodx 1The corresponding calculation formula is:
Figure 926281DEST_PATH_IMAGE019
and calculating the function value of UCB sampling functionf(x 1) And corresponding derivativesg 1', Hessian matrix of second derivativeH 1。
Repeating the above process until the minimum value of the objective function converges, namely:
Figure 806512DEST_PATH_IMAGE020
the iteration point when the minimum function convergesxOptimizing selected leaf profile parameter set by using sampling functionP。
It should be noted that the present embodiment adopts the L-BFGS algorithm to approximate the reciprocal of the Hessian matrixH k -1。
During the optimization process, a large number of leaf geometry samples are generatedBAnd load distribution corresponding to the leaf-shaped geometric sample, and optimal load distribution corresponding to the low-dimensional pneumatic parameter setBThe corresponding database is:
Figure 182130DEST_PATH_IMAGE021
in the formula (I), the compound is shown in the specification,mthe number of the leaf types is the same as the number of the leaf types,kthe leaf-shaped curve can be reduced by adopting a curve fitting mode for the leaf-shaped coordinate points,nthe number of parameter sets is designed for the low dimension.
In this embodiment, the number of leaf patterns is setmThe value of (1) is 150, and the value range covers leaf profiles of various loading forms such as front, middle and rear loading and the like; setting the number of leaf-shaped coordinate pointskIs 64 to ensure the accuracy of the blade profile and the corresponding load distribution.
The database corresponding to the load distribution is as follows:
Figure 540430DEST_PATH_IMAGE022
wherein the content of the first and second substances,lnumber of coordinate points representing load distribution, herelThe number of the values of the leaf profile coordinate points is consistent with 64,mandnmeaning of (2) and leaf geometry samplesBIs consistent in the database.
The optimal load distribution database corresponding to the low-dimensional pneumatic design parameters is as follows:
Figure 449218DEST_PATH_IMAGE023
wherein the content of the first and second substances,knumber of coordinate points representing load distribution, herekThe number of the values of the leaf profile coordinate points is consistent with 64,nsets of parameters are designed for low dimensional pneumatics.
In the present embodiment, the low-dimensional aerodynamic design parameters are basedAAnd optimal load distributionC *The training sample of the optimal load distribution model can be constructed by adopting a matrix splicing modeDThe corresponding formula is:
Figure 500350DEST_PATH_IMAGE024
wherein the content of the first and second substances,knumber of coordinate points representing load distribution, herekThe number of the values of (1) is consistent with the number of the leaf profile coordinate points and is 64.
Step 2, based on the multi-output Gaussian process and the deep neural network, the low-dimensional pneumatic design parameters are calculatedAAs input random variablesxTo distribute the optimum loadC *As output random variablesyConstructing an optimal load distribution model and according to the training sampleDTraining the constructed optimal load distribution model by minimizing a marginal likelihood loss function to obtain a hyperparameter group in the optimal load distribution model, wherein the hyperparameter group is used for determining the trained optimal load distribution model, the optimal load distribution model is composed of a plurality of layers of neurons, and kernel functions of the neuronsK γ Comprises the following steps:
Figure 363264DEST_PATH_IMAGE025
in the formula (I), the compound is shown in the specification,g(x,w) For the intermediate features, the intermediate features are composed of deep neural network and input random variablesxDetermining that the deep neural network has a weight parameter ofwThe feedforward neural network of (1);wfor the weight parameters of the optimal load distribution model,K f defining the similarity between different output tasks for a semi-positive definite matrix;θis a kernel functionK i,j The hyper-parameter of (c);r(. cndot.) is a function of distance,
Figure 525255DEST_PATH_IMAGE026
is the distance mean of the training samples;nis a first preset parameter, and is a second preset parameter,n=1,2,…,5，mis the second preset parameter, and is the second preset parameter,m=2 or 3; the super parameter set at least comprises a weight parameterwHyper-parameterθAnd a semi-positive definite matrixK f 。
Specifically, as shown in fig. 3, in order to improve the accuracy of calculating the total pressure loss of the leaf profile by using the optimal load distribution model, a deep neural network is combined with a multi-output gaussian process MOGP, and a distance function is introduced based on the characteristics of data in training samples in a leaf profile databaser(v) calculating the distance between each data and the intermediate data in the training sample as reference to constructKernel function for each layer of neurons in optimal load distribution modelK i,j Wherein, in the step (A),iis the number of layers of the neuron,jis as followsiIn a layer ofjAnd (4) a neuron.
Low dimensional pneumatic design parametersAThe deep neural network has 3 hidden layers as input, the number of neurons in each layer is 1000/500 and 50, the output layer comprises 8 neurons, and the neurons are input into the MOGP as 8-dimensional intermediate features. Thus, a kernel function of the constructed neuronK i,j Comprises the following steps:
Figure 22970DEST_PATH_IMAGE027
wherein the first preset parameternAnd a second preset parametermAnd randomly selecting the values in the corresponding value range.
Specifically, training the constructed optimal load distribution model by minimizing a marginal likelihood loss function according to a training sample in the leaf database specifically includes:
step 2.1, constructing a marginal likelihood loss function containing a super parameter group according to the optimal load distribution model, wherein the marginal likelihood loss function
Figure 245004DEST_PATH_IMAGE028
Comprises the following steps:
Figure 595214DEST_PATH_IMAGE017
in the formula (I), the compound is shown in the specification,pto marginal probability, i.e.γ，xUnder known conditionsyMarginal probability at the gaussian process model;γin order to be able to set the super-parameter,γ={w,θ,K f }；xinput random variables for optimal load distribution model, design parameters for low-dimensional pneumaticsA；yOutput random variable for optimal load distribution model, optimal load distributionC；σIs the variance of the noise and is,Iis formed by a nuclear envelopeNumber ofK γ Identity matrix with same dimension.
Step 2.2, respectively calculating the weight parameters of the marginal likelihood loss function to the deep neural networkwSemi-positive definite matrixK f And kernel functionsK γ Is a hyper-parameter ofθThe corresponding calculation formula is:
Figure 560896DEST_PATH_IMAGE029
Figure 178697DEST_PATH_IMAGE030
Figure 306053DEST_PATH_IMAGE031
Figure 143559DEST_PATH_IMAGE032
wherein the content of the first and second substances,
Figure 850615DEST_PATH_IMAGE033
the chain rule calculation of a standard back propagation algorithm can be used.
And 2.3, setting a learning rate, and updating the super parameter group in the optimal load distribution model by adopting a gradient descent method, wherein the weight parameters in the super parameter groupwSemi-positive definite matrixK f And hyperparametersθThe iterative update calculation formula of (a) is:
Figure 588502DEST_PATH_IMAGE034
Figure 886759DEST_PATH_IMAGE035
Figure 211561DEST_PATH_IMAGE036
in the formula (I), the compound is shown in the specification,αfor a given learning rate, the learning rate is,θ t is as followstThe hyper-parameters of the kernel function at the next iteration,K f t is as followstThe semi-positive definite matrix at the time of the sub-iteration,w t is as followstWeight parameter at sub-iteration.
Recalculating new marginal likelihood and iteratively updating weight parameters by using the updated super parameter groupwSemi-positive definite matrixK f And hyperparametersθAnd completing model training until the marginal likelihood loss function is minimum.
And 3, giving target low-dimensional pneumatic design parameters, obtaining target optimal load distribution by using the trained optimal load distribution model, and calculating the optimal pneumatic leaf profile corresponding to the target optimal load distribution by using a leaf profile inverse design model constructed based on a deep neural network.
Specifically, as shown in fig. 4, a leaf-type inverse design model is established by using a feedforward neural network FNN, the input of which is load distribution and low-dimensional design parameters, and the output of which is leaf-type geometry. The feedforward neural network FNN is a network structure formed by connecting a plurality of neurons belonging to different network layers in a one-way mode, provides a nonlinear mapping relation between an output and an output, and has an output function of any neurona(x) Comprises the following steps:
Figure 519046DEST_PATH_IMAGE037
in the formula (I), the compound is shown in the specification,σ(. cndot.) is a function of activation,x i is as followsiThe number of the input parameters is one,w i is a function of the corresponding weight or weights,bis a deviation term, wherein the activation functionσ(. cndot.) is the Leaky RELU activation function.
In the leaf-type inverse design model, a square loss function suitable for a real-valued task is used as a parameter learning criterion, and a corresponding calculation formula is as follows:
Figure 845859DEST_PATH_IMAGE038
according to learning criteria, the load distribution database obtained in the above stepsCAnd leaf geometry databaseBAnd as a training sample, carrying out gradient descent training on the network parameters in the leaf type inverse design model through a back propagation algorithm until the square loss function value is continuously descended and converged, and the specific training process is not repeated.
In order to verify the design method in the present embodiment, the low-dimensional aerodynamic design parameters are set as shown in table 2, and the method in the present embodiment is used to design the two-dimensional blade profile of the turbine.
TABLE 2
Figure 580597DEST_PATH_IMAGE039
As shown in fig. 5a, the design method in this embodiment compares the blade profile designed under the operating condition with the Pak-B reference blade profile to obtain the pressure coefficient distribution of the CFD numerical simulation result. The total pressure loss of the blade profile is used as an evaluation index of the operation result of the two methods. It can be seen that the total pressure loss of the blade profile at the design point in table 2 of the Pak-B blade profile design method is 0.0533, while the total pressure loss of the blade profile at the design point in table 2 of the design method in this embodiment is 0.034, which improves the aerodynamic performance of the blade profile in this embodiment by 36%.
FIG. 5B is a comparison of the optimal load distribution for the low dimensional design parameters and the Pak-B reference profile, where it can be seen that the load distribution of the design profile remains laminar at the suction surface, while the Pak-B profile has separation bubbles at 75% -93% of the axial position of the suction surface, which causes a rapid increase in profile loss and poor aerodynamic performance due to separation. Therefore, the load distribution of the blade profile designed in the embodiment is better than the coincidence distribution of the Pak-B blade profile, and is the optimal load distribution of the blade profile.
As shown in FIG. 6, this embodiment further compares the total pressure loss of the blade profile and the Pak-B blade profile at different angles of attack in the range of-45, 30. The blade profile designed by the embodiment can keep a low loss value in the range of attack angles of-40 degrees to 15 degrees, and the loss value is smaller than the load distribution of the Pak-B blade profile.
As shown in FIG. 7, this embodiment further compares the Reynolds number range of 10,000 to 200,000, and the total pressure loss of the blade profile of this embodiment design blade profile and the blade profile of Pak-B blade profile, it can be seen that the blade profile of this embodiment design has better aerodynamic performance in the wide Reynolds number working range.
Meanwhile, the two-dimensional blade profile geometry of the turbine corresponding to the designed optimal load distribution can be automatically obtained within 1 second. Compared with other existing design methods which take several hours or even several days, the design period of the blade profile can be greatly shortened.
The technical scheme of the invention is explained in detail in the above with reference to the accompanying drawings, and the invention provides a real-time high-precision aerodynamic design method for a low-pressure turbine blade profile of an aircraft engine, which comprises the following steps: step 1, generating a leaf profile geometric sample according to a given leaf profile parameter value range and a low-dimensional pneumatic design parameter, calculating optimal load distribution when the total pressure loss of the leaf profile is minimum through CFD, and generating a leaf profile database; step 2, constructing an optimal load distribution model based on a multi-output Gaussian process and a deep neural network, and training the optimal load distribution model through a minimized marginal likelihood loss function according to training samples in a leaf database to obtain a super parameter set in the optimal load distribution model; and 3, calculating the target optimal load distribution of the target low-dimensional pneumatic design parameters according to the trained optimal load distribution model, and calculating the optimal pneumatic blade profile corresponding to the target optimal load distribution by using a blade profile inverse design model. According to the technical scheme, the precision and the efficiency of the turbine blade profile pneumatic design are improved, and the geometric design period of the turbine blade profile is shortened.
The steps in the invention can be sequentially adjusted, combined and deleted according to actual requirements.
The units in the device of the invention can be merged, divided and deleted according to actual requirements.
Although the present invention has been disclosed in detail with reference to the accompanying drawings, it is to be understood that such description is merely illustrative of and not restrictive on the application of the present invention. The scope of the invention is defined by the appended claims and may include various modifications, adaptations and equivalents of the invention without departing from its scope and spirit.

Claims (4)

1. A low-pressure turbine blade profile aerodynamic design method based on optimal load distribution model optimization is characterized by comprising the following steps:
step 1, generating a geometric sample of the blade profile according to a given value range of the blade profile parameters and low-dimensional pneumatic design parametersBCalculating the optimal load distribution when the total pressure loss of the blade profile is minimum through CFD to generate a blade profile database;
step 2, constructing an optimal load distribution model based on a multi-output Gaussian process and a deep neural network, training the optimal load distribution model through a minimum marginal likelihood loss function according to training samples in the leaf database to obtain a super parameter set in the optimal load distribution model, wherein the super parameter set is used for determining the trained optimal load distribution model,
wherein the optimal load distribution model is composed of a plurality of layers of neurons, the kernel functions of whichK γ Comprises the following steps:
Figure 253674DEST_PATH_IMAGE001
in the formula (I), the compound is shown in the specification,g(x,w) In order to be an intermediate feature,wthe neural network weight parameter for the optimal load distribution model,r=|x-x' is two groups of random variablesxAndxthe distance of (a) to (b),K f is a semi-positive definite matrix and is provided with a positive definite matrix,θis a kernel functionK γ Is determined by the parameter (c) of (c),r(. cndot.) is a function of distance,
Figure 5729DEST_PATH_IMAGE002
to be the distance average of the training samples,nis a first preset parameter, and is a second preset parameter,n=1,2,…,5，mis the second preset parameter, and is the second preset parameter,m=2 or 3, the super parameter group includes at least weight parameterwHyper-parameterθAnd a semi-positive definite matrixK f ；
And 3, calculating the target optimal load distribution of the target low-dimensional pneumatic design parameters according to the trained optimal load distribution model, and calculating the optimal pneumatic blade profile corresponding to the target optimal load distribution by using a blade profile inverse design model.
2. The method for designing the aerodynamic shape of the low-pressure turbine blade optimized based on the optimal load distribution model according to claim 1, wherein the step 1 specifically comprises the following steps:
step 1.1, generating an initial blade profile parameter set by utilizing a sampling function and a blade profile parameterization method in a given blade profile parameter value range according to the low-dimensional pneumatic design parametersPAnd the leaf geometry sampleB；
Step 1.2, taking the low-dimensional pneumatic design parameters as boundary conditions, and according to the initial blade profile parameter groupPPerforming CFD calculation on the leaf-shaped geometric sample to obtain the leaf-shaped geometric sampleBCorresponding load distribution and total pressure loss of the blade profile;
step 1.3, utilizing Bayesian optimization iteration to generate the set of leaf parameterPAnd (4) re-executing the step 1.1 until the load distribution with the minimum total pressure loss of the blade profile is obtained, and recording the load distribution as the optimal load distribution.
3. The aerodynamic design method of a low-pressure turbine blade profile optimized based on an optimal load distribution model as claimed in claim 2, wherein the step 1.3 specifically comprises:
step 1.3.1, establishing a Gaussian process model of the blade profile parameter group P and the blade profile total pressure loss, and utilizing a training sample setMTraining the Gaussian process model, and updating the hyper-parameters in the Gaussian process model;
step 1.3.2, based on the trained Gaussian process model, in the given value range of the leaf parameter, optimizing and selecting a leaf parameter group P by using a sampling function, re-executing the step 1.1, and calculating the leaf parameter groupPUpdating the training sample set according to the corresponding load distribution and total pressure loss of the blade profileMAnd obtaining the optimal load distribution when the total pressure loss of the blade profile is minimum.
4. The method for designing a low-pressure turbine blade profile based on optimization of an optimal load distribution model according to claim 1, wherein in the step 2, the training of the optimal load distribution model through minimization of a marginal likelihood loss function according to the training samples in the blade profile database specifically comprises:
step 2.1, constructing a marginal likelihood loss function containing the super parameter group according to the optimal load distribution model, wherein a calculation formula of the marginal likelihood loss function is as follows:
Figure 765875DEST_PATH_IMAGE003
in the formula (I), the compound is shown in the specification,pin order to be a marginal probability,γin order to be able to set the super-parameter,xfor the input random variables of the optimal load distribution model,yfor the output random variables of the optimal load distribution model,σis the variance of the noise and is,Iis a function of a kernelK γ Identity matrices of the same dimension;
step 2.2, respectively calculating the weight parameter w and the semi-positive definite matrix of the marginal likelihood loss functionK f And the hyper-parameterθPartial derivatives of (d);
and 2.3, setting a learning rate, and updating the super parameter group in the optimal load distribution model by adopting a gradient descent method so as to train the optimal load distribution model.
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