CN115688317B - Bayesian optimization and GCN-based shape optimization design method for turbine wheel disc of gas turbine - Google Patents

Bayesian optimization and GCN-based shape optimization design method for turbine wheel disc of gas turbine

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CN115688317B
CN115688317B CN202211387360.2A CN202211387360A CN115688317B CN 115688317 B CN115688317 B CN 115688317B CN 202211387360 A CN202211387360 A CN 202211387360A CN 115688317 B CN115688317 B CN 115688317B
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optimization
wheel
stress
wheel disc
design
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CN115688317A (en
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谢永慧
仇志龙
王崇宇
傅柏生
张荻
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Xian Jiaotong University
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Xian Jiaotong University
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Abstract

本发明基于贝叶斯优化和GCN的燃机透平轮盘形状优化设计方法，包括：步骤一，采用Bezier曲线参数化燃气轮机透平轮盘，确定并构建设计变量优化空间；步骤二，在优化空间内采样，利用样本数据建立几何模型并分别进行有限元计算分析，获取最大径向变形量、最大应力值和质量数据，构建优化设计数据库；步骤三，将数据库中的子数据集分别进行前处理；步骤四，构建图卷积神经网络，使用步骤三所得的数据集进行训练，得到由几何参数到位移场、应力场分布的轮盘预测模型；步骤五，采用贝叶斯优化方法结合训练好的轮盘预测模型进行自动寻优及目标优化，得到轮盘几何结构最终优化设计方案。本发明具有重要的工程应用效益和推广价值。

The present invention utilizes Bayesian optimization and GCN to optimize the shape of a gas turbine turbine disk. The method comprises the following steps: first, parameterizing the gas turbine disk using Bezier curves to determine and construct an optimization space for design variables; second, sampling within the optimization space, using the sample data to establish a geometric model and perform finite element analysis to obtain maximum radial deformation, maximum stress, and mass data, thereby constructing an optimized design database; third, pre-processing each sub-dataset in the database; fourth, constructing a graph convolutional neural network and training it using the data set obtained in step three to obtain a disk prediction model from geometric parameters to displacement and stress field distributions; and fifth, using Bayesian optimization combined with the trained disk prediction model to perform automatic optimization and target optimization to obtain a final optimized design solution for the disk geometry. This invention has significant engineering application benefits and promotional value.

Description

Bayesian optimization and GCN-based shape optimization design method for turbine wheel disc of gas turbine
Technical Field
The invention relates to the technical field of power equipment structural design, in particular to a gas turbine wheel disc shape optimization design method based on Bayesian optimization and GCN.
Background
The turbine wheel disc of the gas turbine is an important component part of the gas turbine, and the performance quality of the turbine wheel disc influences the use and the safety of the whole machine. In order to increase the reliability and structural integrity of the wheel disc, the weight of the wheel disc can be obviously reduced by the optimized design of the wheel disc, and the stress of key parts of the wheel disc is reduced.
Limited by computational resources, in the disclosed procedures and methods for optimizing various types of wheels, the static stress level of the wheel is of greater concern than the dynamic characteristics can be considered simultaneously. This process is very time consuming because several finite element calculations need to be performed during the optimization process. On one hand, the existing wheel disc shape optimization method is optimized based on limited design parameters, and geometric parameters are relatively fixed, so that the wheel disc shape change boundary is narrower, and generalization is not facilitated. It is therefore necessary to develop new wheel shape parameterization methods. On the other hand, the traditional method mainly adopts non-gradient algorithms such as Monte Carlo, simulated annealing or genetic algorithm in the optimizing process, and the algorithms depend on a large number of calculation samples, are easy to fall into local optimal values, and are not beneficial to optimization. It is therefore necessary to develop new wheel shape optimization methods.
In recent years, various optimization methods based on machine learning and deep learning are successfully applied to the fields of pneumatic design optimization, structural vibration intensity optimization, topology optimization and the like, and a better solution idea is provided for engineering optimization problems. Research results show that compared with the traditional optimization algorithm, the optimization method based on machine learning and deep learning has the characteristics of rapidness, flexibility and high robustness. However, at present, researches and reports on machine learning and deep learning as optimization of the shape of a fuel turbine wheel disc are fresh.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a gas turbine wheel shape optimization design method based on Bayesian optimization and GCN (graph convolution neural network), which adopts Bezier curves to parameterize wheel types, considers the temperature gradient load from high-temperature high-pressure fuel gas, and fits the actual working condition of the wheel, and has the characteristics of short design period, wide optimization range, effective and reliable optimization design result, and important engineering application benefit and popularization value.
The invention is realized by adopting the following technical scheme:
a shape optimization design method of a turbine wheel disc of a gas turbine based on Bayesian optimization and GCN comprises the following steps:
Firstly, carrying out parameterization modeling on a turbine wheel disc geometry of a gas turbine to be optimized by adopting a Bezier curve, determining geometric parameters serving as design variables, determining a value range of the geometric parameters, and constructing an optimization space of the geometric design variables of the wheel disc;
Sampling design variables in a design domain based on an optimization space of the geometric design variables of the wheel disc, establishing a geometric model of the wheel disc by using sample data, respectively carrying out finite element calculation and analysis according to the geometric model to obtain maximum radial deformation, maximum stress value and quality data of the wheel disc, and constructing a geometric structure optimization design database of the wheel disc;
respectively carrying out normalization operation on data in the wheel disc geometric structure optimization design database, and dividing the data into a training set and a verification set according to the proportion of 7:3 after random scrambling, wherein the training set and the verification set are used as a data set of a graph convolution neural network;
step four, constructing a graph convolution neural network, and training by using the data set in the step three to obtain a wheel disc prediction model distributed from geometric parameters to a displacement field and a stress field;
and fifthly, performing target optimization on the wheel disc by adopting a Bayesian optimization method and combining a trained wheel disc prediction model, and performing automatic optimization on a wheel disc combined structure to obtain a final optimal design scheme of the wheel disc geometric structure.
The invention is further improved in that the first step specifically comprises:
the Bezier curve is adopted to parameterize the wheel disc molded line, and the expression is as follows:
Wherein P (t) is a point on a Bezier curve, P i is a Bezier curve control point, B i,n (t) is a Bernstein base function, t is a curve point generation parameter, n is a Bezier curve order, and t is continuously changed in a range of [0,1] to determine a corresponding Bezier curve after the curve order n and the control point P i are determined;
And marking the transverse and longitudinal sitting of the ith control point as [ x i,yi ], taking the coordinates of all the control points as geometric design variables, and constructing an optimization space of the geometric design variables of the wheel disc, wherein the value range of the geometric design variables is +/-20% of the initial value.
The invention further improves that the turbine wheel disc part of the gas turbine is of an axisymmetric structure, and the two-dimensional optimization design is carried out aiming at the wheel surface molded line, namely, when the geometric structure of the wheel disc is optimized, the wheel surface molded line is designed, and the displacement and stress distribution conditions of the wheel surface molded line are considered.
The invention is further improved in that the Bezier curves with different orders are used for parameterizing different parts of the wheel disc.
The invention is further improved in that the second step specifically comprises:
Sampling in an optimization space formed by coordinates of each intermediate control point of a Bezier curve by using a Latin hypercube sampling method to obtain a wheel disc sample set S, establishing the Bezier curve for each sample in the sample set S to obtain a wheel disc geometric model, calling finite element calculation software to perform grid division and numerical calculation to obtain a wheel disc displacement field f 1 and a stress field f 2, obtaining the maximum radial deformation delta u x,max and the maximum stress value sigma max of the wheel disc, simultaneously calculating the corresponding wheel disc mass m by combining wheel disc material parameters, deriving the wheel disc grid node coordinates C= [ X, y ], and jointly forming a database [ X ] = { S, C, f 1,f2,Δux,max,σmax, m } of the optimization design of the wheel disc geometric structure by using design variables and target parameters.
The invention is further improved in that the third step specifically comprises:
normalizing the data set according to the formula:
Wherein [ X j ] is the j-th dataset in the database, min and Max respectively represent the maximum value and the minimum value of each dimension data in the corresponding dataset, epsilon=1×10 -6 is a small amount;
generating random numbers will normalize the data set Randomly sorting and dividing the training sets into training sets according to the proportion of 7:3And a verification set
The invention is further improved in that the step four specifically comprises:
Construction of displacement field and stress field prediction model GNet based on graph convolution neural network, specifically, GNet is composed of an input layer, a graph convolution layer and an output layer, wherein the input layer is composed of a full-connection layer and an activation function, the graph convolution layer is composed of a 6-layer graph convolution operator and an activation function, the output layer is a 1-layer graph convolution operator, GNet is input with a sample set S and wheel disc profile grid node coordinates C, and the predicted displacement field of the wheel disc profile is output Stress fieldThe network mapping relation is as follows:
in the formula, The method comprises the steps of obtaining a predicted displacement field or stress field of a wheel disc molded surface, wherein F is a graph convolution map, S is single sample data comprising the abscissa of a Bezier curve control point, C is the grid node coordinate of the single sample, and Θ is a parameter to be learned of a network;
utilizing a data set Training GNet, utilizing a datasetVerification is performed during the training process.
The invention further improves the method, based on the obtained predicted stress field, for monitoring and judging the stress concentration phenomenon of the key part of the wheel disc structure, and specifically comprises the following steps:
Wherein, sigma loc,max is the local stress maximum value of the key part of the structure, sigma loc,m is the local stress average value, sigma th is the stress threshold value for stress concentration monitoring, and K is the local structure stress concentration factor;
Firstly, determining a stress threshold sigma th based on turbine wheel disc materials of a gas turbine and working conditions of high temperature, high temperature gradient and high rotating speed, secondly, monitoring stress values of key parts of a wheel disc structure based on an obtained predicted stress field, judging the stress concentration degree if the maximum stress value sigma loc,max exceeds sigma th, and finally, calculating a local structure stress concentration factor K by sigma loc,max and sigma loc,m to represent the stress concentration degree of the key parts.
The invention is further improved in that the fifth step specifically comprises:
And carrying out loop iteration on the wheel disc molded line design by combining the high-precision wheel disc displacement field stress field prediction model obtained by training through a Bayesian optimization method, wherein the Bayesian optimization carries out automatic optimization on the wheel disc molded line data by taking a priori function and an acquisition function as cores, the prediction model carries out displacement field stress field prediction according to the newly generated wheel disc molded line to obtain displacement field distribution, maximum radial deformation and stress field distribution and maximum stress, simultaneously calculates the mass of the corresponding wheel disc, and continuously carries out recommendation and evaluation under the target requirement that the maximum radial deformation is smaller than the allowable radial deformation, the maximum stress is smaller than the allowable stress and the mass is minimum, thereby finally obtaining the optimal design scheme of the wheel disc structure.
The invention is further improved in that the prior function in Bayesian optimization adopts widely used Gaussian process regression, the acquisition function adopts an improved STABLE form STABLE-EI of expected increment EI widely used in standard Bayesian optimization, and the improved STABLE form STABLE-EI has good robustness, so that the Bayesian optimization process is easier to obtain a global optimal solution;
Wherein ,vt＝σt(x,ΣX);zt＝[mt(x,∑X)-ωσt,a(x,∑x)-f(x+)]/vt;Φ(z) is a standard normal cumulative distribution function, phi (z) is a standard normal probability density function, m (x) is a mean function, omega is a weight for penalizing the midpoint of the unstable region, f (x) is a function from gaussian process regression, x +＝arg maxf(xi.
Compared with the prior art, the invention has at least the following beneficial technical effects:
The invention provides a wheel disc structure optimization design method based on Bayesian optimization and graph convolution neural network by integrating a plurality of prior art and carrying out improvement and innovation on the gas turbine wheel disc structure optimization design method. The parameterized model, sampling calculation, database establishment, high-precision wheel disc displacement field stress field prediction model GNet obtained by training and automatic optimization by combining Bayesian optimization with the prediction model can be realized through one script in the whole process, no manual participation or intervention is needed in the middle, and the method is simple and efficient; compared with the traditional wheel disc optimization method, the method provided by the invention improves the whole flow of the wheel disc structural design, and has the advantages of stronger geometric structure expression capability, larger optimization exploration breadth and shorter optimization iteration period.
Furthermore, the invention adopts the Bezier curve to carry out subsection parameterization on the wheel disc molded line, the description capability of the required optimized curve is strong and the curve is continuous and smooth on the premise of ensuring the geometric parameters of the key part of the wheel disc, and compared with the traditional parameterization method, the invention can generate complex molded lines more conveniently and realize the fine description of the geometric shape of the wheel disc.
Furthermore, the Latin hypercube sampling method is adopted to obtain the sample set, the sampled sample set has good representativeness and descriptive property on the optimization space, and a database which is enough to support and train out a high-precision displacement field stress field prediction model can be obtained under the condition of the minimum sample number.
Furthermore, the invention constructs the stress field prediction model of the wheel disc displacement field based on the graph convolutional neural network, can realize the field prediction of any irregular grid, obviously is difficult to realize the regular division of the finite element grid for the physical model with complex molded lines such as the wheel disc, and fundamentally solves the problem that the convolutional neural network can only process the regular grid.
Further, the invention provides a method for monitoring and judging stress concentration phenomena at key parts of a structure, corresponding stress thresholds are determined based on material parameters and working conditions of a turbine wheel disc of a gas turbine, firstly, local stress concentration conditions are monitored, if the stress concentration conditions exceed the thresholds, local stress concentration degrees are represented by calculating stress concentration factors, and the local stress concentration conditions at the key parts are considered while the geometric structure is optimized.
Furthermore, the invention adopts the Bayesian optimization method which takes the Gaussian process regression as the prior function and the STABLE-EI as the acquisition function to carry out automatic optimization, wherein the proxy model constructed by the Gaussian process regression has high precision, the STABLE-EI can converge the function optimization to a STABLE peak value, and the turbine wheel disc geometry of the gas turbine meeting the design target can be rapidly found.
Furthermore, a Bayesian optimization method with widely verified performance in parameter optimization is combined with a high-precision wheel disc displacement field stress field prediction model constructed based on a graph convolution neural network, and the optimal design of the wheel disc structure with the lightest mass under the conditions of meeting the maximum radial deformation and allowable stress is realized in an optimization space.
In conclusion, the invention has important engineering significance and wide application prospect.
Drawings
FIG. 1 is a general flow chart of the method for optimizing the design of a turbine disk shape of a gas turbine based on Bayesian optimization and GCN of the present invention.
Fig. 2 is a schematic view of parameterization of an axisymmetric cross-section profile of an embodiment of a wheel disc.
FIG. 3 is a schematic diagram of the overall architecture of a wheel displacement field stress field prediction model constructed based on a graph convolution neural network.
FIG. 4 is a graph of the loss function of an example displacement field stress field predictive model training process.
FIG. 5 is a comparison cloud of predicted displacement field stress fields versus actual displacement field stress fields of an embodiment.
FIG. 6 is a plot of predicted displacement field stress field grid node scattergrams during an embodiment optimization process.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1, the method for optimizing and designing the shape of the turbine wheel disc of the gas turbine based on bayesian optimization and GCN provided by the invention comprises the following steps:
1. performing parameterization modeling on the turbine wheel disc geometry of the gas turbine to be optimized by adopting a Bezier curve, determining the geometric parameter serving as a design variable, and simultaneously determining the value range of the geometric parameter to construct an optimization space of the geometric design variable of the wheel disc;
The expression of the Bezier curve is:
Wherein P (t) is a point on a Bezier curve, P i is a Bezier curve control point, B i,n (t) is a Bernstein basis function, t is a curve point generation parameter, n is a Bezier curve order, and t continuously changes in a range of [0,1] to determine a corresponding Bezier curve after the curve order n and the control point P i are determined.
The invention adopts the Bezier curve to describe the wheel disc molded line instead of the traditional method of describing the wheel disc molded line by using discrete points, and the discrete point method can describe the molded line simply, but does not have the advantages of less control parameters of the Bezier curve, flexible adjustment and infinite continuity, and a large number of data points are needed to describe the complex shape of the wheel disc finely.
The method for sectionally parameterizing the wheel disc adopts Bezier curves with different orders to parameterize different parts of the wheel disc, and combines good shape control capability of the Bezier curves, so that the wheel disc has enough optimization possibility on the premise of ensuring that geometrical parameters of key parts such as end face teeth are not changed.
Considering that the turbine wheel of the gas turbine has a combination relation between stages, the head and tail control points of the Bezier curve are fixed, so that the applicability of the geometric shape of the wheel established in the optimization process is ensured, and the number of design variables is reasonably reduced.
Referring to FIG. 2, considering that the turbine wheel disk part of the gas turbine is in an axisymmetric structure, two-dimensional optimization design is only carried out for the wheel surface molded line, the head and tail control points of the Bezier curve are fixed in consideration of the combination relation between the stages of the turbine wheel disk of the gas turbine, the transverse and longitudinal seats of the ith control point are marked as [ x i,yi ] in the middle of the Bezier curve, the coordinates of all the control points are used as geometric design variables, and the value range is +/-20% of the initial value, so that a design variable optimization space is formed. And parameterizing different parts of the wheel disc by adopting Bezier curves with different orders respectively.
2. Sampling in an optimization space formed by coordinates of each intermediate control point of a Bezier curve by using a Latin hypercube sampling method to obtain a wheel disc sample set S, establishing the Bezier curve for each sample in the sample set S to obtain a wheel disc geometric model, and calling finite element calculation software to perform grid division and unidirectional thermosetting coupling numerical calculation to obtain a wheel disc displacement field f 1 and a stress field f 2, thereby obtaining the maximum radial deformation delta u x,max and the maximum stress value sigma max of the wheel disc, simultaneously obtaining the corresponding wheel disc mass m by combining the wheel disc material parameters, deriving the wheel disc grid node coordinates C= [ X, y ], and jointly forming a database [ X ] = { S, C, f 1,f2,Δux,max,σmax, m } of the optimization design of the wheel disc geometric structure by using design variables and target parameters.
According to the invention, the Latin hypercube sampling method is adopted to sample the design variable in the optimization space, and the obtained sample set can fully describe the optimization space, so that the constructed wheel disc database is beneficial to training a prediction model with good performance.
It should be noted that the radial deformation of the wheel disc mentioned in the present invention refers to the radial displacement difference of the rim portion.
The unidirectional thermosetting coupling is performed during the finite element calculation analysis, namely, the temperature gradient load from the high-temperature fuel gas under the working condition of the wheel disc is considered. Most of the prior researches on optimal design of the wheel disc do not consider the heat load, which is obviously unreasonable, so that the obtained optimal result meets the design requirement only when no heat load exists, the actual operability is not achieved, or the design margin is too large, the optimal design is not called optimal, and the true optimal structure can be obtained only by optimizing under the condition of fitting the actual running condition of the wheel disc.
3. Normalizing the data set according to the formula:
Where [ X j ] is the j-th dataset in the database, min and Max represent the maximum and minimum values of the respective dimension data in the corresponding dataset, respectively, and ε=1×10 -6 is a small amount.
Generating random numbers will normalize the data setRandomly sorting and dividing the training sets into training sets according to the proportion of 7:3And a verification set
4. Displacement field stress field prediction model GNet is constructed based on a graph roll-up neural network, and with reference to fig. 3, gnet is composed of an input layer, a graph roll-up layer and an output layer, wherein the input layer is composed of a full-connection layer and an activation function GELU, the graph roll-up layer is composed of a 6-layer graph convolution operator and an activation function GELU, and the output layer is a 1-layer graph convolution operator. GNet inputting the sample set S and the wheel disc profile grid node coordinate C, and outputting the predicted displacement field of the wheel disc profileStress fieldThe network mapping relation is as follows:
in the formula, The method comprises the steps of obtaining a predicted displacement field or stress field of a wheel disc molded surface, wherein F is a graph convolution map, S is single sample data comprising the abscissa of a Bezier curve control point, C is grid node coordinates of a single sample, and Θ is a parameter to be learned of a network.
Using the data set obtained in step 3AndTraining is carried out, smooth average absolute deviation SmoothL is adopted as a loss function in the training process, the optimization algorithm of the network model adopts a stable version Adamax of the self-adaptive moment estimation algorithm, the initial learning rate is 0.001, the learning rate in the training process adopts a step-down strategy, the learning rate in the [100,150,200] step is respectively reduced to one tenth of that before, and finally the high-precision displacement field stress field prediction model GNet is obtained through training.
GNet adopts a Gaussian deviation linear unit GELU as an activation function, random regularization is introduced into the activation function, probability description is carried out on neuron input, and overfitting can be effectively restrained, and generalization capability of a model is enhanced. The method has the advantages that the wheel disc stress field prediction model is built based on the graph convolution neural network, the direct prediction of the displacement value and the stress value of the grid node of the wheel disc finite element model can be realized, the method can be suitable for any grid structure, the defect that the field prediction is not performed by using the convolution neural network and is based on regular grid nodes is overcome, and the method has extremely strong friendliness to field analysis and calculation of complex molded line physical models such as the turbine wheel disc of the gas turbine.
The obtained predicted displacement field and stress field are not intermediate quantities in the optimization process, and have important significance, on one hand, the visualized field information has strong interpretability which is not available in other proxy models, and on the other hand, the method monitors and judges the stress concentration phenomenon possibly occurring at the key parts of the wheel disc in the optimization design process by means of the field information.
Based on the obtained predicted stress field, monitoring and judging the stress concentration phenomenon of the key part of the wheel disc structure, specifically comprising the following steps:
In the formula, sigma loc,max is a local stress maximum value of a key part of the structure, sigma loc,m is a local stress average value, sigma th is a stress threshold value for stress concentration monitoring, and K is a local structure stress concentration factor.
Firstly, determining a stress threshold sigma th based on turbine wheel disc materials of a gas turbine and working conditions of high temperature, high temperature gradient and high rotating speed, secondly, monitoring stress values of key parts of a wheel disc structure based on an obtained predicted stress field, judging the stress concentration degree if the maximum stress value sigma loc,max exceeds sigma th, and finally, calculating a local structure stress concentration factor K by sigma loc,max and sigma loc,m to represent the stress concentration degree of the key parts.
5. And carrying out loop iteration of the wheel disc molded line design by adopting a Bayesian optimization method with a prior function of Gaussian process regression and an acquisition function of STABLE-EI and combining the high-precision wheel disc displacement field stress field prediction model GNet obtained through the training. The Bayesian optimization automatically optimizes the wheel disc molded line data, the prediction model predicts the stress field of the displacement field according to the newly generated wheel disc molded line to obtain the distribution of the displacement field, the maximum radial deformation and the stress field distribution and the maximum stress value,
Simultaneously, the mass of the wheel disc can be obtained by combining material parameters, and under the target requirements that the maximum radial deformation is smaller than the allowable radial deformation, the maximum stress is smaller than the allowable stress and the mass is minimum, and no obvious stress concentration phenomenon exists, the optimal structural design scheme of the wheel disc is finally obtained by continuously recommending and evaluating.
The stress field prediction of the wheel disc displacement field is carried out by using a high-precision prediction model obtained based on graph convolution neural network training, so that a time-consuming process that finite element software needs to be repeatedly called for analysis in the optimizing process in the traditional method is replaced, and a quick, accurate and efficient scheme is provided for the optimization design of the wheel disc structure.
The STABLE-EI is an improved STABLE form based on any variance of an expected increment EI widely used for acquiring a function in standard Bayesian optimization, and the function can be optimized to a STABLE region in an unstable region around a false peak so as to converge to a STABLE peak value, so that the method has good robustness, and the Bayesian optimization process is easier to obtain a globally optimal solution.
Wherein ,vt＝σt(x,ΣX);zt＝[mt(x,∑X)-ωσt,a(x,∑x)-f(x+)]/vt;Φ(z) is a standard normal cumulative distribution function, phi (z) is a standard normal probability density function, m (x) is a mean function, omega is a weight for penalizing the midpoint of the unstable region, f (x) is a function from gaussian process regression, and x+= argmaxf (x i).
The STABLE-EI is an acquisition function based on arbitrary variance improvement, and an unstable region around a false spike can optimize the function to a STABLE region to converge to a STABLE peak with the same computational complexity as EI in standard Bayesian optimization without having a tendency to converge to an unstable spike as in standard Bayesian optimization.
When a Bayesian optimization method is used for generating new sample points in the optimizing process, a high-precision prediction model obtained based on graph convolution neural network training is used for predicting the stress field of the wheel disc displacement field, so that the time-consuming process that finite element software is required to be repeatedly called for calculation in the optimizing process in the traditional method is replaced, and a quick, accurate and efficient scheme is provided for the optimization design of the wheel disc structure.
Examples
The invention relates to a shape optimization design method of a turbine wheel disc of a gas turbine based on Bayesian optimization and GCN, which is used for optimally designing the turbine wheel disc of the gas turbine, and specifically comprises the following steps:
1. As shown in FIG. 2, in order to ensure that geometric parameters of key parts such as end face teeth are unchanged, an 8-order Bezier curve and a 5-order Bezier curve are respectively adopted to carry out sectional parametric modeling on the wheel disc.
The expression of the Bezier curve is:
Wherein P (t) is a point on a Bezier curve, P i is a Bezier curve control point, B i,n (t) is a Bernstein basis function, t is a curve point generation parameter, n is a Bezier curve order, and t continuously changes in a range of [0,1] to determine a corresponding Bezier curve after the curve order n and the control point P i are determined.
Considering that the turbine wheel of the gas turbine has a combination relation between the stages, the head and tail control points of the Bezier curve are fixed, so that the number of variable control points in the middle of the Bezier curve is 7 and 4 respectively, thereby realizing fine description of the part to be optimized and fully excavating the optimization depth. And marking the transverse and longitudinal coordinates of the ith control point in the middle of the Bezier curve as [ x i,yi ], taking the coordinates of all the control points as geometric design variables, wherein the value ranges of the transverse coordinates and the longitudinal coordinates are respectively +/-10% and +/-20% of the initial values, and the value ranges of the design variables are shown in a table 1 to form an optimization space of the geometric design variables of the wheel disc.
Table 1 roulette design variable values
2. Sampling in an optimization space formed by coordinates of each intermediate control point of a Bezier curve by using a Latin hypercube sampling method to obtain a wheel disc sample set S, establishing the Bezier curve for each sample in the sample set S to obtain a wheel disc geometric model, and calling finite element calculation software to perform grid division and unidirectional thermosetting coupling numerical calculation to obtain a wheel disc displacement field f 1 and a stress field f 2, thereby obtaining the maximum radial deformation delta u x,max and the maximum stress value sigma max of the wheel disc, simultaneously obtaining the corresponding wheel disc mass m by combining the wheel disc material parameters, deriving the wheel disc grid node coordinates C= [ X, y ], and jointly forming a database [ X ] { S, C=, f 1,f2,Δux,max,σmax, m } of the optimization design of the wheel disc geometric structure by using design variables and target parameters.
3. Normalizing the data set according to the formula:
Where [ X j ] is the j-th dataset in the database, min and Max represent the maximum and minimum values of the respective dimension data in the corresponding dataset, respectively, and ε=1×10 -6 is a small amount.
Generating random numbers will normalize the data setRandomly sorting and dividing the training sets into training sets according to the proportion of 7:3And a verification set
4. Using the data set obtained in step3AndThe training of the displacement field stress field prediction model GNet (refer to fig. 3) is completed, the loss curve of the training process refers to fig. 4, and the cloud image of the predicted displacement field stress field and the real displacement field stress field obtained by the prediction model refers to fig. 5, wherein the real field, the predicted field and the error field are respectively from left to right, and the radial displacement field and the stress field are respectively from top to bottom, so that the prediction effect can be seen to be excellent.
Based on the obtained predicted stress field, monitoring and judging the stress concentration phenomenon of the key part of the wheel disc structure, specifically comprising the following steps:
In the formula, sigma loc,max is a local stress maximum value of a key part of the structure, sigma loc,m is a local stress average value, sigma th is a stress threshold value for stress concentration monitoring, and K is a local structure stress concentration factor.
Firstly, determining a stress threshold sigma th based on turbine wheel disc materials of a gas turbine and working conditions of high temperature, high temperature gradient and high rotating speed, secondly, monitoring stress values of key parts of a wheel disc structure based on an obtained predicted stress field, judging the stress concentration degree if the maximum stress value sigma loc,max exceeds sigma th, and finally, calculating a local structure stress concentration factor K by sigma loc,max and sigma loc,m to represent the stress concentration degree of the key parts.
5. And carrying out loop iteration of the wheel disc molded line design by adopting a Bayesian optimization method with a prior function of Gaussian process regression and an acquisition function of STABLE-EI and combining the high-precision wheel disc displacement field stress field prediction model GNet obtained through the training.
The Bayesian optimization automatically optimizes the wheel disc molded line data, the prediction model GNet predicts the stress field of the displacement field according to the newly generated wheel disc molded line, the displacement field distribution, the maximum radial deformation amount, the stress field distribution and the maximum stress value are obtained, the predicted displacement field stress field grid node scatter diagram of the new geometric structure in the optimization design process is respectively the radial displacement field and the stress field from top to bottom according to the figure 6, and meanwhile, the quality of the wheel disc can be obtained by combining material parameters.
And referring to various values of the optimization constraint parameters and the target parameters of the wheel disc shown in the table 2, continuously recommending and evaluating the values under the target requirements that the maximum radial deformation is smaller than the allowable radial deformation, the maximum stress is smaller than the allowable stress and the mass is minimum and no obvious stress concentration phenomenon exists, so that the optimal structural design scheme of the wheel disc is finally obtained.
TABLE 2 optimization constraint parameters and target parameters for roulette
While the invention has been described in detail in the foregoing general description and with reference to specific embodiments thereof, it will be apparent to one skilled in the art that modifications and improvements can be made thereto. Accordingly, such modifications or improvements may be made without departing from the spirit of the invention and are intended to be within the scope of the invention as claimed.

Claims (10)

1.基于贝叶斯优化和GCN的燃机透平轮盘形状优化设计方法，其特征在于，包括以下步骤：1. A gas turbine turbine disk shape optimization design method based on Bayesian optimization and GCN is characterized by comprising the following steps: 步骤一，采用Bezier曲线将待优化的燃气轮机透平轮盘几何结构进行参数化建模，确定作为设计变量的几何参数，同时确定其取值范围，构建轮盘几何设计变量的优化空间；Step 1: Use Bezier curves to parametrically model the geometric structure of the gas turbine wheel to be optimized, determine the geometric parameters as design variables, and determine their value ranges to construct the optimization space of the wheel geometry design variables; 步骤二，基于轮盘几何设计变量的优化空间，在设计域内对设计变量进行采样，利用样本数据建立轮盘几何模型，依据几何模型分别进行有限元计算分析，获取轮盘的最大径向变形量、最大应力值和质量数据，构建轮盘几何结构优化设计数据库；Step 2: Based on the optimization space of the wheel's geometric design variables, sample the design variables within the design domain, use the sample data to establish a wheel geometry model, perform finite element analysis based on the geometric model, obtain the maximum radial deformation, maximum stress value, and mass data of the wheel, and construct a wheel geometry structure optimization design database; 步骤三，将轮盘几何结构优化设计数据库中的数据分别进行归一化操作，并在随机打乱之后按照比例7：3分为训练集和验证集，作为图卷积神经网络的数据集；Step 3: Normalize the data in the wheel geometry optimization design database and randomly shuffle them into a training set and a validation set in a ratio of 7:3 to serve as the dataset for the graph convolutional neural network. 步骤四，构建图卷积神经网络，使用步骤三的数据集进行训练，得到由几何参数到位移场、应力场分布的轮盘预测模型；Step 4: Build a graph convolutional neural network and train it using the data set from step 3 to obtain a wheel prediction model from geometric parameters to displacement and stress field distributions. 步骤五，采用贝叶斯优化方法结合训练好的轮盘预测模型对轮盘进行目标优化，对轮盘结合结构进行自动寻优，得到轮盘几何结构最终优化设计方案。Step five: Use the Bayesian optimization method combined with the trained roulette prediction model to optimize the roulette target, automatically optimize the roulette combination structure, and obtain the final optimized design scheme of the roulette geometric structure. 2.根据权利要求1所述的基于贝叶斯优化和GCN的燃机透平轮盘形状优化设计方法，其特征在于，步骤一具体包括：2. The gas engine turbine disk shape optimization design method based on Bayesian optimization and GCN according to claim 1, wherein step 1 specifically comprises: 采用Bezier曲线参数化轮盘型线，表达式如下：The wheel profile is parameterized using Bezier curves, and the expression is as follows: 式中，P(t)为Bezier曲线上的点；Pi为Bezier曲线控制点；Bi,n(t)为Bernstein基函数；t为曲线点生成参数；n为Bezier曲线阶数；曲线阶数n和控制点Pi确定之后，t在[0,1]范围内连续变化确定相应的Bezier曲线；Where P(t) is a point on the Bezier curve; Pi is a control point of the Bezier curve; Bi ,n (t) is a Bernstein basis function; t is a parameter for generating the curve point; and n is the order of the Bezier curve. After the order n and the control point Pi are determined, t is continuously varied in the range [0,1] to determine the corresponding Bezier curve. 将第i个控制点的横纵坐标记为[xi,yi]，将所有控制点的坐标作为几何设计变量，取值范围为初始值的±20％，构建轮盘几何设计变量的优化空间。The horizontal and vertical coordinates of the i-th control point are marked as [ xi , yi ]. The coordinates of all control points are used as geometric design variables with a value range of ±20% of the initial value to construct the optimization space of the wheel's geometric design variables. 3.根据权利要求2所述的基于贝叶斯优化和GCN的燃机透平轮盘形状优化设计方法，其特征在于，燃气轮机透平轮盘部分为轴对称结构，针对轮面型线进行二维优化设计，即在对轮盘几何结构进行优化时，设计轮盘型线、考虑轮盘型面的位移和应力分布情况即可。3. The gas turbine impeller shape optimization design method based on Bayesian optimization and GCN according to claim 2 is characterized in that the gas turbine impeller portion is an axisymmetric structure, and a two-dimensional optimization design is performed on the wheel surface profile, that is, when optimizing the wheel geometry, the wheel profile is designed and the displacement and stress distribution of the wheel surface are considered. 4.根据权利要求2所述的基于贝叶斯优化和GCN的燃机透平轮盘形状优化设计方法，其特征在于，分别采用不同阶数的Bezier曲线对轮盘的不同部位进行参数化。4. The gas turbine wheel disc shape optimization design method based on Bayesian optimization and GCN according to claim 2 is characterized in that different parts of the wheel disc are parameterized using Bezier curves of different orders. 5.根据权利要求2所述的基于贝叶斯优化和GCN的燃机透平轮盘形状优化设计方法，其特征在于，步骤二具体包括：5. The gas engine turbine disk shape optimization design method based on Bayesian optimization and GCN according to claim 2, wherein step 2 specifically comprises: 采用拉丁超立方采样方法在由Bezier曲线各个中间控制点坐标构成的优化空间内进行采样，得到轮盘样本集S，对样本集S内的每个样本建立Bezier曲线得到轮盘几何模型，调用有限元计算软件进行网格划分和数值计算，得到轮盘位移场f1和应力场f2，由此得到轮盘的最大径向变形量Δux,max和最大应力值σmax，同时结合轮盘材料参数计算得到相应的轮盘质量m，导出轮盘网格节点坐标C＝[x,y]，由设计变量和目标参数共同构成轮盘几何结构优化设计的数据库[X]＝{S,C,f1,f2,Δux,max,σmax,m}。The Latin hypercube sampling method is used to sample in the optimization space formed by the coordinates of the intermediate control points of the Bezier curve to obtain the wheel sample set S. A Bezier curve is established for each sample in the sample set S to obtain the wheel geometric model. Finite element calculation software is used for meshing and numerical calculation to obtain the wheel displacement field f1 and stress field f2 . From this, the maximum radial deformation Δu x,max and the maximum stress value σ max of the wheel are obtained. At the same time, the corresponding wheel mass m is calculated based on the wheel material parameters, and the wheel grid node coordinates C = [x, y] are derived. The design variables and target parameters together constitute the database [X] = {S, C, f1 , f2 , Δu x,max , σ max , m} for the optimal design of the wheel geometry. 6.根据权利要求5所述的基于贝叶斯优化和GCN的燃机透平轮盘形状优化设计方法，其特征在于，步骤三具体包括：6. The gas engine turbine disk shape optimization design method based on Bayesian optimization and GCN according to claim 5, wherein step three specifically comprises: 根据公式对数据集进行归一化操作：Normalize the data set according to the formula: 式中，[Xj]为数据库中的第j个数据集；Min和Max分别表示相应数据集中各个维度数据的最大值和最小值；ε＝1×10-6，为小量；Where [X j ] is the jth dataset in the database; Min and Max represent the maximum and minimum values of each dimension in the corresponding dataset, respectively; ε = 1 × 10 -6 , which is a small value; 生成随机数将归一化之后的数据集进行随机排序，按照7:3的比例划分为训练集和验证集 Generate random numbers to normalize the dataset Randomly sort and divide into training sets according to the ratio of 7:3 and validation set 7.根据权利要求6所述的基于贝叶斯优化和GCN的燃机透平轮盘形状优化设计方法，其特征在于，步骤四具体包括：7. The gas engine turbine disk shape optimization design method based on Bayesian optimization and GCN according to claim 6, wherein step 4 specifically comprises: 基于图卷积神经网络构建位移场和应力场预测模型GNet，具体地，GNet由输入层、图卷积层和输出层构成，其中输入层由全连接层和激活函数组成，图卷积层由6层图卷积算子和激活函数组成，输出层为1层图卷积算子；GNet输入样本集S和轮盘型面网格节点坐标C，输出轮盘型面的预测位移场和应力场网络映射关系为：The displacement field and stress field prediction model GNet is constructed based on the graph convolutional neural network. Specifically, GNet consists of an input layer, a graph convolution layer, and an output layer. The input layer consists of a fully connected layer and an activation function, the graph convolution layer consists of 6 layers of graph convolution operators and activation functions, and the output layer is a 1-layer graph convolution operator. GNet inputs the sample set S and the grid node coordinates C of the roulette surface, and outputs the predicted displacement field of the roulette surface. and stress field The network mapping relationship is: 式中，为轮盘型面的预测位移场或者应力场；F为图卷积映射；S为包括Bezier曲线控制点横纵坐标的单个样本数据；C为单个样本的网格节点坐标；Θ为网络的待学习参数；Where, is the predicted displacement field or stress field of the wheel surface; F is the graph convolution mapping; S is a single sample data including the horizontal and vertical coordinates of the Bezier curve control points; C is the grid node coordinate of a single sample; Θ is the parameter to be learned of the network; 利用数据集对GNet进行训练，利用数据集在训练过程中进行验证。Leveraging Datasets Train GNet using the dataset Validation is performed during training. 8.根据权利要求7所述的基于贝叶斯优化和GCN的燃机透平轮盘形状优化设计方法，其特征在于，基于得到的预测应力场，进行轮盘结构关键部位应力集中现象监测判别，具体如下：8. The gas turbine disc shape optimization design method based on Bayesian optimization and GCN according to claim 7 is characterized in that, based on the obtained predicted stress field, stress concentration phenomena in key parts of the disc structure are monitored and identified as follows: 式中，σloc,max为结构关键部位所在局部应力最大值；σloc,m为该局部应力平均值；σth为进行应力集中监测的应力阈值；K为局部结构应力集中因数；Where σloc ,max is the maximum local stress value at the key part of the structure; σloc ,m is the average local stress value; σth is the stress threshold for stress concentration monitoring; K is the local structural stress concentration factor; 首先基于燃气轮机透平轮盘材料及高温、高温度梯度、高转速的工作条件确定应力阈值σth；其次基于得到的预测应力场对轮盘结构关键部位应力值进行监测，若最大应力值σloc,max超过σth，则需要进行应力集中程度判别；最后，由σloc,max和σloc,m计算局部结构应力集中因数K，表征该关键部位应力集中程度。First, the stress threshold σ th is determined based on the gas turbine wheel material and the operating conditions of high temperature, high temperature gradient, and high speed. Second, the stress values at key parts of the wheel structure are monitored based on the obtained predicted stress field. If the maximum stress value σ loc,max exceeds σ th , the degree of stress concentration needs to be determined. Finally, the local structural stress concentration factor K is calculated from σ loc,max and σ loc,m to characterize the degree of stress concentration at this key part. 9.根据权利要求7所述的基于贝叶斯优化和GCN的燃机透平轮盘形状优化设计方法，其特征在于，步骤五具体包括：9. The gas engine turbine disk shape optimization design method based on Bayesian optimization and GCN according to claim 7, wherein step five specifically comprises: 采用贝叶斯优化方法结合上述训练得到的高精度轮盘位移场应力场预测模型进行轮盘型线设计的循环迭代，其中贝叶斯优化以先验函数和采集函数为核心对轮盘型线数据进行自动寻优，预测模型根据新生成的轮盘型线进行位移场应力场预测，得到位移场分布及最大径向变形量和应力场分布及最大应力，同时计算得到相应轮盘的质量，在最大径向变形量小于许可径向变形量、最大应力小于许用应力、质量最小的目标要求下，不断进行推荐和评估，最终得到轮盘结构的最优设计方案。The Bayesian optimization method is combined with the high-precision wheel displacement field and stress field prediction model obtained through the above training to perform cyclic iteration of wheel profile design. The Bayesian optimization automatically optimizes the wheel profile data with the prior function and acquisition function as the core. The prediction model predicts the displacement field and stress field based on the newly generated wheel profile, and obtains the displacement field distribution and maximum radial deformation, the stress field distribution and maximum stress. At the same time, the mass of the corresponding wheel is calculated. Under the target requirements of maximum radial deformation less than the allowable radial deformation, maximum stress less than the allowable stress, and minimum mass, continuous recommendations and evaluations are made to finally obtain the optimal design scheme of the wheel structure. 10.根据权利要求9所述的基于贝叶斯优化和GCN的燃机透平轮盘形状优化设计方法，其特征在于，贝叶斯优化中先验函数采用广泛使用的高斯过程回归，采集函数采用标准贝叶斯优化中广泛使用的期望增量EI的改进稳定形式STABLE-EI，具有良好的鲁棒性，使得贝叶斯优化过程更易于获得全局最优解；10. The gas turbine disk shape optimization design method based on Bayesian optimization and GCN according to claim 9 is characterized in that the prior function in Bayesian optimization adopts the widely used Gaussian process regression, and the acquisition function adopts the improved stable form of expected increment (EI) widely used in standard Bayesian optimization, STABLE-EI, which has good robustness and makes it easier for the Bayesian optimization process to obtain the global optimal solution; 式中，vt＝σt(x,Σx)；zt＝[mt(x,∑X)-ωσt,a(x,∑x)-f(x+)]/vt；Φ(z)为标准正态积累分布函数；φ(z)为标准正态概率密度函数；m(x)为均值函数；ω为用于惩罚不稳定区域中点的权重；f(x)是来自高斯过程回归的函数；x+＝argmaxf(xi)。where v t = σ t (x, Σ x ); z t = [m t (x, ∑ X ) - ωσ t, a (x, ∑ x ) - f (x + )] / v t ; Φ(z) is the standard normal cumulative distribution function; φ(z) is the standard normal probability density function; m(x) is the mean function; ω is the weight used to penalize midpoints in unstable regions; f(x) is the function from Gaussian process regression; and x + = argmaxf( xi ).
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