Shape Optimization Design Method for Gas Turbine Disc Based on Bayesian Optimization and GCN

Abstract

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

Technical Field

[0001] The present invention relates to the technical field of power equipment structure design, and in particular to a gas turbine turbine wheel disc shape optimization design method based on Bayesian optimization and GCN. Background Art

[0002] The turbine wheel is a critical component of a gas turbine, and its performance impacts the overall operation and safety of the turbine. To enhance wheel reliability and structural integrity, optimized wheel design can significantly reduce wheel weight and lower stress in key wheel areas.

[0003] Due to limited computing resources, the various publicly available programs and methods for roulette optimization focus more on the static stress level of the roulette, and fail to consider dynamic characteristics at the same time. This is because several finite element calculations are required during the optimization process, which is very time-consuming. On the one hand, existing roulette shape optimization methods are based on finite design parameters for optimization, and the geometric parameters are relatively fixed. Therefore, the boundary of roulette shape variation is narrow, which is not conducive to generalization. Therefore, it is necessary to develop a new roulette shape parameterization method. On the other hand, traditional methods mainly use non-gradient algorithms such as Monte Carlo, simulated annealing, or genetic algorithms in the optimization process. These algorithms rely on a large number of calculation samples and are prone to falling into local optimal values, which is not conducive to optimization. Therefore, it is necessary to develop a new roulette shape optimization method.

[0004] In recent years, various optimization methods based on machine learning and deep learning have been successfully applied to fields such as aerodynamic design optimization, structural vibration strength optimization, and topology optimization, providing improved solutions to engineering optimization problems. Research results show that compared with traditional optimization algorithms, optimization methods based on machine learning and deep learning are faster, more flexible, and more robust. However, there are currently few studies or reports on the use of machine learning and deep learning for gas turbine disk shape optimization. Summary of the Invention

[0005] The purpose of the present invention is to address the deficiencies of the existing technology and provide a gas turbine turbine wheel shape optimization design method based on Bayesian optimization and GCN (graph convolutional neural network). The wheel profile is parameterized by Bezier curves, while taking into account the temperature gradient load from high-temperature and high-pressure gas on the turbine wheel during operation, and adapting to the actual working conditions of the wheel. At the same time, it has the characteristics of short design cycle, wide optimization range, effective and reliable optimization design results, and has important engineering application benefits and promotion value.

[0006] The present invention is achieved by adopting the following technical solutions:

[0007] The gas turbine disc shape optimization design method based on Bayesian optimization and GCN includes the following steps:

[0008] 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;

[0009] 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;

[0010] 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.

[0011] 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.

[0012] 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.

[0013] A further improvement of the present invention is that step one specifically comprises:

[0014] The wheel profile is parameterized using Bezier curves, and the expression is as follows:

[0015]

[0016] Where P(t) is a point on the Bezier curve; P i is the control point of the Bezier curve; B i,n (t) is the Bernstein basis function; t is the curve point generation parameter; n is the Bezier curve order; the curve order n and the control point P i After determination, t is continuously varied in the range [0,1] to determine the corresponding Bezier curve;

[0017] The horizontal and vertical coordinates of the i-th control point are marked as [x i ,y i ], the coordinates of all control points are taken as geometric design variables with a value range of ±20% of the initial value, and the optimization space of the wheel geometric design variables is constructed.

[0018] A further improvement of the present invention is that the turbine wheel part of the gas turbine 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.

[0019] A further improvement of the present invention is that different parts of the wheel are parameterized using Bezier curves of different orders.

[0020] A further improvement of the present invention is that step 2 specifically includes:

[0021] The Latin hypercube sampling method is used to sample in the optimization space formed by the coordinates of each intermediate control point 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. The finite element calculation software is called for meshing and numerical calculation to obtain the wheel displacement field f1 and stress field f2, thereby obtaining the maximum radial deformation Δu of the wheel. x,max and the maximum stress value σ max At the same time, the corresponding wheel mass m is calculated by combining the wheel material parameters, and the wheel grid node coordinates C = [x, y] are derived. The database of wheel geometry optimization design [X] = {S, C, f1, f2, Δu x,max ,σ max ,m}.

[0022] A further improvement of the present invention is that step three specifically includes:

[0023] Normalize the data set according to the formula:

[0024]

[0025] In the formula, [X j ] is the jth data set in the database; Min and Max represent the maximum and minimum values of each dimension data in the corresponding data set respectively; ε = 1×10 -6 , for a small amount;

[0026] Generate random numbers to normalize the dataset Randomly sort and divide into training sets according to the ratio of 7:3 and validation set

[0027] A further improvement of the present invention is that step 4 specifically includes:

[0028] 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:

[0029]

[0030] 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;

[0031] Leveraging Datasets Train GNet using the dataset Validation is performed during training.

[0032] A further improvement of the present invention is to monitor and identify stress concentration phenomena at key parts of the wheel disc structure based on the predicted stress field, as follows:

[0033]

[0034] Where σ loc,max is the maximum local stress at the key part of the structure; σ loc,m is the average value of the local stress; σ th is the stress threshold for stress concentration monitoring; K is the local structural stress concentration factor;

[0035] First, the stress threshold σ is determined based on the gas turbine wheel material and the working conditions of high temperature, high temperature gradient and high speed. th Secondly, based on the predicted stress field, the stress values of key parts of the wheel structure are monitored. If the maximum stress value σ loc,max Exceed σ th , then it is necessary to judge the degree of stress concentration; finally, by σ loc,max and σ loc,m Calculate the local structural stress concentration factor K to characterize the degree of stress concentration in the key part.

[0036] A further improvement of the present invention is that step five specifically includes:

[0037] 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.

[0038] A further improvement of the present invention is that the prior function in Bayesian optimization adopts the widely used Gaussian process regression, and the acquisition function adopts the improved stable form STABLE-EI of the expected increment EI widely used in standard Bayesian optimization, which has good robustness and makes the Bayesian optimization process easier to obtain the global optimal solution;

[0039]

[0040] 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 the midpoint in the unstable region; f(x) is the function from Gaussian process regression; x + =arg maxf(x i ).

[0041] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0042] By integrating multiple existing technologies, the present invention improves and innovates the method for optimizing the design of gas turbine wheel disc structures, and proposes a wheel disc structure optimization design method based on Bayesian optimization and graph convolutional neural networks. The present invention involves parameterizing the model, sampling and calculating to establish a database, training to obtain a high-precision wheel displacement field and stress field prediction model GNet, and combining Bayesian optimization with the prediction model for automatic optimization. The entire process can be achieved end-to-end through a single script, without any human participation or intervention in the middle, which is simple and efficient. At the same time, compared with traditional wheel disc optimization methods, the method proposed in the present invention improves the entire wheel disc structure design process, with stronger geometric structure expression capabilities, a wider range of optimization exploration, and a shorter optimization iteration cycle.

[0043] Furthermore, the present invention uses Bezier curves to perform segmented parameterization of the wheel profile. While ensuring the geometric parameters of key parts of the wheel, the invention has a strong ability to describe the required optimized curve and the curve is continuous and smooth. Compared with traditional parameterization methods, it can more conveniently generate complex profiles and achieve a detailed description of the wheel's geometric shape.

[0044] Furthermore, the present invention adopts the Latin hypercube sampling method to obtain a sample set. The sampled samples are well representative and descriptive of the optimization space, and a database sufficient to support the training of a high-precision displacement field and stress field prediction model can be obtained with as few samples as possible.

[0045] Furthermore, the present invention constructs a wheel displacement field and stress field prediction model based on a graph convolutional neural network, which can realize field prediction of any irregular grid. It is obviously difficult to achieve regular division of finite element grids for physical models with complex lines such as wheel. This fundamentally solves the problem that convolutional neural networks can only process regular grids.

[0046] Furthermore, the present invention proposes a method for monitoring and identifying stress concentration phenomena in key parts of a structure. The corresponding stress threshold is determined based on material parameters and the operating conditions of the gas turbine turbine wheel. First, the local stress concentration situation is monitored. If the threshold is exceeded, the degree of local stress concentration is characterized by calculating the stress concentration factor. The local stress concentration situation in key parts is taken into account while optimizing the geometric structure.

[0047] Furthermore, the present invention adopts a Bayesian optimization method with Gaussian process regression as the prior function and STABLE-EI as the acquisition function for automatic optimization. The proxy model constructed by Gaussian process regression has high accuracy, and STABLE-EI can converge the function optimization to a stable peak value, which can quickly find the gas turbine wheel geometry that meets the design objectives.

[0048] Furthermore, the Bayesian optimization method, whose performance in parameter optimization has been widely verified, is combined with a high-precision wheel displacement field and stress field prediction model built based on a graph convolutional neural network to achieve the optimal design of the wheel structure with the lightest mass that meets the conditions of maximum radial deformation and allowable stress within the optimization space.

[0049] In summary, the present invention has important engineering significance and broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is an overall flow chart of the gas engine turbine wheel shape optimization design method based on Bayesian optimization and GCN of the present invention.

[0051] Figure 2 It is a parametric schematic diagram of the axisymmetric cross-section profile of the wheel in the embodiment.

[0052] Figure 3 Schematic diagram of the overall architecture of the wheel displacement field and stress field prediction model built based on graph convolutional neural network.

[0053] Figure 4 This is the loss function curve of the displacement field and stress field prediction model training process in the embodiment.

[0054] Figure 5 This is a comparison cloud diagram of the predicted displacement field and stress field in the embodiment and the actual displacement field and stress field.

[0055] Figure 6 This is a scatter plot of the grid nodes for predicting the displacement field and stress field during the optimization process of the embodiment. DETAILED DESCRIPTION

[0056] The present invention will be further described below with reference to the accompanying drawings.

[0057] Reference Figure 1 The present invention provides a gas turbine wheel disk shape optimization design method based on Bayesian optimization and GCN, comprising the following steps:

[0058] 1. Use Bezier curves to parametrically model the geometry of the gas turbine disk to be optimized, determine the geometric parameters as design variables, and also determine their value ranges to construct the optimization space of the disk geometry design variables;

[0059] The expression of Bezier curve is:

[0060]

[0061] Where P(t) is a point on the Bezier curve; P i is the control point of the Bezier curve; B i,n(t) is the Bernstein basis function; t is the curve point generation parameter; n is the Bezier curve order; the curve order n and the control point P i After determination, t is continuously varied in the range [0,1] to determine the corresponding Bezier curve.

[0062] The present invention adopts Bezier curve to describe the roulette wheel profile, rather than the traditional method of using discrete points to describe the roulette wheel profile. Although the discrete point method can describe the profile simply and clearly, it does not have the advantages of Bezier curve with few control parameters, flexible adjustment and infinite continuity. It often requires a large number of data points to have a detailed description of complex shapes such as roulette wheels.

[0063] Bezier curves of different orders are used to parameterize different parts of the wheel. Combined with the good shape control ability of Bezier curves, this piecewise parameterization method makes it possible to optimize the wheel sufficiently without changing the geometric parameters of key parts such as the end teeth.

[0064] Taking into account the combination relationship between stages of the gas turbine wheel, the first and last control points of the Bezier curve are fixed. This not only ensures the applicability of the wheel geometry established in the optimization process, but also reasonably reduces the number of design variables.

[0065] Reference Figure 2 Considering that the turbine wheel of the gas turbine is an axisymmetric structure, only the wheel profile is optimized in two dimensions. Considering that there is a combination relationship between stages of the turbine wheel of the gas turbine, the first and last control points of the Bezier curve are fixed. The horizontal and vertical coordinates of the i-th control point in the middle of the Bezier curve are marked as [x i ,y i ], the coordinates of all control points are used as geometric design variables, with a value range of ±20% of the initial value, to form the design variable optimization space. Different Bezier curves of different orders are used to parameterize different parts of the wheel.

[0066] 2. Use the Latin hypercube sampling method to sample in the optimization space formed by the coordinates of each intermediate control point of the Bezier curve to obtain the wheel sample set S. For each sample in the sample set S, establish a Bezier curve to obtain the wheel geometric model. Call the finite element calculation software for meshing and unidirectional thermo-structural coupling numerical calculation to obtain the wheel displacement field f1 and stress field f2, thereby obtaining the maximum radial deformation Δu of the wheel x,max and the maximum stress value σ maxAt the same time, the corresponding wheel mass m can be calculated by combining the wheel material parameters, and the wheel grid node coordinates C = [x, y] are derived. The database of wheel geometry optimization design [X] = {S, C, f1, f2, Δu x,max ,σ max ,m}, the above whole process can be realized by autonomous calculation through a script.

[0067] The present invention adopts the Latin hypercube sampling method to sample the design variables in the optimization space. The obtained sample set can fully describe the optimization space, so the constructed roulette database is conducive to training a prediction model with good performance.

[0068] It should be pointed out that the radial deformation of the wheel mentioned in the present invention refers to the radial displacement difference of the wheel rim.

[0069] During the finite element analysis, one-way thermal-solid coupling was performed, accounting for the temperature gradient loads from the high-temperature gas under the disc's operating conditions. Most existing studies on disc optimization design fail to consider thermal loads, which is clearly inappropriate. The resulting optimization results either only meet design requirements without thermal loads and lack practical operability, or have excessive design margins, making them insufficiently optimal. Only by optimizing under the disc's actual operating conditions can a truly optimal structure be obtained.

[0070] 3. Normalize the data set according to the formula:

[0071]

[0072] In the formula, [X j ] is the jth data set in the database; Min and Max represent the maximum and minimum values of each dimension data in the corresponding data set respectively; ε = 1×10 -6 , for a small amount.

[0073] Generate random numbers to normalize the dataset Randomly sort and divide into training sets according to the ratio of 7:3 and validation set

[0074] 4. Construct the displacement field and stress field prediction model GNet based on graph convolutional neural network, refer to Figure 3 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 GELU, the graph convolution layer consists of 6 layers of graph convolution operators and activation function GELU, and the output layer is a single layer of graph convolution operators. GNet inputs a 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:

[0075]

[0076] 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.

[0077] Using the data set obtained in step 3 and The training was carried out, and the smooth mean absolute deviation SmoothL1 was used as the loss function during the training process. The optimization algorithm of the network model adopted the stable version of the adaptive moment estimation algorithm Adamax. The initial learning rate was 0.001. During the training process, the learning rate adopted a step-by-step decline strategy. At steps [100, 150, 200], the learning rate was reduced to one tenth of the previous one. Finally, a high-precision displacement field and stress field prediction model GNet was obtained through training.

[0078] GNet's activation function uses the Gaussian biased linear unit (GELU). This activation function incorporates random regularization, providing a probabilistic description of neuron inputs. This effectively suppresses overfitting and enhances the model's generalization capabilities. A wheel disk stress field prediction model based on a graph convolutional neural network (GCNN) enables direct prediction of displacement and stress values at the mesh nodes of the wheel disk's finite element model. This model can adapt to any mesh structure and avoids the drawback of using convolutional neural networks for field prediction, which requires regular mesh nodes. This makes it particularly suitable for field analysis and calculations involving complex linear physical models, such as gas turbine wheels.

[0079] The predicted displacement field and stress field obtained are not intermediate quantities in the optimization process. They are of great significance. On the one hand, the visualized field information has strong interpretability that other proxy models do not have. On the other hand, the present invention uses field information to monitor and identify stress concentration phenomena that may occur in key parts of the wheel during the optimization design process.

[0080] Based on the predicted stress field, the stress concentration phenomenon in the key parts of the wheel disc structure is monitored and identified as follows:

[0081]

[0082] Where σ loc,max is the maximum local stress at the key part of the structure; σ loc,m is the average value of the local stress; σ th is the stress threshold for stress concentration monitoring; K is the local structure stress concentration factor.

[0083] First, the stress threshold σ is determined based on the gas turbine wheel material and the working conditions of high temperature, high temperature gradient and high speed. th Secondly, based on the predicted stress field, the stress values of key parts of the wheel structure are monitored. If the maximum stress value σ loc,max Exceed σ th , then it is necessary to judge the degree of stress concentration; finally, by σ loc,max and σ loc,m Calculate the local structural stress concentration factor K to characterize the degree of stress concentration in the key part.

[0084] 5. Using the Bayesian optimization method with Gaussian process regression as the prior function and STABLE-EI as the acquisition function, combined with the high-precision wheel displacement and stress field prediction model GNet obtained from the above training, the wheel profile design is iterated. Bayesian optimization automatically optimizes the wheel profile data. The prediction model predicts the displacement and stress fields based on the newly generated wheel profile, and obtains the displacement field distribution and maximum radial deformation, as well as the stress field distribution and maximum stress value.

[0085] At the same time, the mass of the wheel can be obtained by combining the material parameters. Under the target requirements of maximum radial deformation less than the allowable radial deformation, maximum stress less than the allowable stress, minimum mass, and no obvious stress concentration phenomenon, continuous recommendations and evaluations are made to finally obtain the optimal structural design scheme of the wheel.

[0086] A high-precision prediction model trained based on a graph convolutional neural network is used to predict the displacement and stress fields of the wheel. This replaces the time-consuming process of repeatedly calling finite element software for analysis in the traditional optimization process, providing a fast, accurate and efficient solution for the optimization design of the wheel structure.

[0087] STABLE-EI is an improved stable form of the expected incremental EI based on arbitrary variance, which is widely used in the acquisition function of standard Bayesian optimization. It can optimize the function to a stable region in the unstable region around the pseudo-spike and thus converge to a stable peak. It has good robustness, making it easier for the Bayesian optimization process to obtain the global optimal solution.

[0088]

[0089] Where, v t =σ t (x,Σ X );z t =[m t (x,∑ X )-ωσ t,a (x,∑ x )-f(x + )] / v tΦ(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 the midpoint of the unstable region; f(x) is the function from Gaussian process regression; x + = argmaxf(x i ).

[0090] STABLE-EI is an improved acquisition function based on arbitrary variance. In the unstable region around the pseudo-spike, the function can be optimized to the stable region, thereby converging to a stable peak. It has the same computational complexity as EI in standard Bayesian optimization and does not tend to converge to unstable spikes like standard Bayesian optimization.

[0091] During the optimization process, when the Bayesian optimization method generates new sample points, a high-precision prediction model trained based on a graph convolutional neural network is used to predict the displacement and stress fields of the wheel. This replaces the time-consuming process of repeatedly calling finite element software for calculations in the traditional optimization process, providing a fast, accurate and efficient solution for the optimization design of the wheel structure.

[0092] Example

[0093] The gas turbine wheel disk shape optimization design method based on Bayesian optimization and GCN of the present invention is used to optimize the design of a gas turbine wheel disk, as follows:

[0094] 1. If Figure 2 As shown in the figure, in order to ensure that the geometric parameters of key parts such as the end teeth remain unchanged, the 8th-order Bezier curve and the 5th-order Bezier curve are used to perform segmented parametric modeling of the wheel.

[0095] The expression of Bezier curve is:

[0096]

[0097] Where P(t) is a point on the Bezier curve; P i is the control point of the Bezier curve; B i,n (t) is the Bernstein basis function; t is the curve point generation parameter; n is the Bezier curve order; the curve order n and the control point P i After determination, t is continuously varied in the range [0,1] to determine the corresponding Bezier curve.

[0098] Considering the combination relationship between the stages of the gas turbine wheel, the first and last control points of the Bezier curve are fixed, so the number of variable control points in the middle of the Bezier curve is 7 and 4 respectively, so as to achieve a fine description of the part to be optimized and fully explore the optimization depth. The horizontal and vertical coordinates of the i-th control point in the middle of the Bezier curve are marked as [xi ,y i ], the coordinates of all control points are taken as geometric design variables, and the ranges of horizontal and vertical coordinates are ±10% and ±20% of the initial values respectively. The ranges of design variables are shown in Table 1, which constitute the optimization space of the wheel geometric design variables.

[0099] Table 1 Roulette wheel design variable values

[0100]

[0101] 2. Use the Latin hypercube sampling method to sample in the optimization space formed by the coordinates of each intermediate control point of the Bezier curve to obtain the wheel sample set S. For each sample in the sample set S, establish a Bezier curve to obtain the wheel geometric model. Call the finite element calculation software for meshing and unidirectional thermal-solid coupling numerical calculation to obtain the wheel displacement field f1 and stress field f2, thereby obtaining the maximum radial deformation Δu of the wheel x,max and the maximum stress value σ max At the same time, the corresponding wheel mass m can be calculated by combining the wheel material parameters, and the wheel grid node coordinates C = [x, y] are derived. The database of wheel geometry optimization design [X] = {S, C, f1, f2, Δu x,max ,σ max ,m}, the above whole process can be realized by autonomous calculation through a script.

[0102] 3. Normalize the data set according to the formula:

[0103]

[0104] In the formula, [X j ] is the jth data set in the database; Min and Max represent the maximum and minimum values of each dimension data in the corresponding data set respectively; ε = 1×10 -6 , for a small amount.

[0105] Generate random numbers to normalize the dataset Randomly sort and divide into training sets according to the ratio of 7:3 and validation set

[0106] 4. Use the data set obtained in step 3 and Complete the displacement field stress field prediction model GNet (refer to Figure 3 ) training, the training process loss curve reference Figure 4 , the predicted displacement field and stress field obtained by the prediction model are compared with the cloud map of the real displacement field and stress field Figure 5, where from left to right they are the true field, predicted field and error field, and from top to bottom they are the radial displacement field and stress field. It can be seen that the prediction effect is excellent.

[0107] Based on the predicted stress field, the stress concentration phenomenon in the key parts of the wheel disc structure is monitored and identified as follows:

[0108]

[0109] Where σ loc,max is the maximum local stress at the key part of the structure; σ loc,m is the average value of the local stress; σ th is the stress threshold for stress concentration monitoring; K is the local structure stress concentration factor.

[0110] First, the stress threshold σ is determined based on the gas turbine wheel material and the working conditions of high temperature, high temperature gradient and high speed. th Secondly, based on the predicted stress field, the stress values of key parts of the wheel structure are monitored. If the maximum stress value σ loc,max Exceed σ th , then it is necessary to judge the degree of stress concentration; finally, by σ loc,max and σ loc,m Calculate the local structural stress concentration factor K to characterize the degree of stress concentration in the key part.

[0111] 5. The Bayesian optimization method with Gaussian process regression as the prior function and STABLE-EI as the acquisition function is combined with the high-precision wheel displacement field and stress field prediction model GNet obtained by the above training to perform cyclic iteration of wheel profile design.

[0112] Bayesian optimization automatically optimizes the wheel profile data. The prediction model GNet predicts the displacement field and stress field based on the newly generated wheel profile, and obtains the displacement field distribution and maximum radial deformation as well as the stress field distribution and maximum stress value. The predicted displacement field and stress field grid node scatter plot of the new geometric structure in the optimization design process is referenced. Figure 6 , from top to bottom are the radial displacement field and stress field respectively; at the same time, the mass of the wheel can be obtained by combining the material parameters.

[0113] Referring to the values of the disk optimization constraint parameters and target parameters shown in Table 2, under the target requirements of maximum radial deformation less than the allowable radial deformation, maximum stress less than the allowable stress, minimum mass, and no obvious stress concentration, continuous recommendations and evaluations were made to finally obtain the optimal structural design scheme of the disk.

[0114] Table 2 Roulette optimization constraint parameters and target parameters

[0115]

[0116] Although the present invention has been described in detail above using general descriptions and specific embodiments, it will be apparent to those skilled in the art that modifications and improvements may be made based on the present invention. Therefore, such modifications and improvements, which do not depart from the spirit of the present invention, are intended to be within the scope of protection claimed herein.

Claims

1. A gas turbine wheel shape optimization design method based on Bayesian optimization and GCN is characterized by: The following steps are involved: 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; 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; 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. 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. 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. The gas turbine wheel disc shape optimization design method based on Bayesian optimization and GCN according to claim 1 is characterized in that: Step 1 specifically includes: The wheel profile is parameterized using Bezier curves, and the expression is as follows: Where P(t) is a point on the Bezier curve; P i is the control point of the Bezier curve; B i,n (t) is the Bernstein basis function; t is the curve point generation parameter; n is the Bezier curve order; the curve order n and the control point P i After determination, t is continuously varied in the range [0,1] to determine the corresponding Bezier curve; The horizontal and vertical coordinates of the i-th control point are marked as [x i ,y i ], the coordinates of all control points are taken as geometric design variables with a value range of ±20% of the initial value, and the optimization space of the wheel geometric design variables is constructed.

3. The gas turbine wheel shape optimization design method based on Bayesian optimization and GCN according to claim 2 is characterized in that: The turbine wheel part of the gas turbine 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. The gas turbine wheel shape optimization design method based on Bayesian optimization and GCN according to claim 2 is characterized in that: Bezier curves of different orders are used to parameterize different parts of the wheel.

5. The gas turbine wheel shape optimization design method based on Bayesian optimization and GCN according to claim 2 is characterized in that: Step 2 specifically includes: The Latin hypercube sampling method is used to sample in the optimization space formed by the coordinates of each intermediate control point 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. The finite element calculation software is called for meshing and numerical calculation to obtain the wheel displacement field f1 and stress field f2, thereby obtaining the maximum radial deformation Δu of the wheel. x,max and the maximum stress value σ max At the same time, the corresponding wheel mass m is calculated by combining the wheel material parameters, and the wheel grid node coordinates C = [x, y] are derived. The database of wheel geometry optimization design [X] = {S, C, f1, f2, Δu x,max ,σ max ,m}.

6. The gas turbine wheel disc shape optimization design method based on Bayesian optimization and GCN according to claim 5 is characterized in that: Step three specifically includes: Normalize the data set according to the formula: In the formula, [X j ] is the jth data set in the database; Min and Max represent the maximum and minimum values of each dimension data in the corresponding data set respectively; ε = 1×10 -6 , for a small amount; 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. The gas turbine wheel disc shape optimization design method based on Bayesian optimization and GCN according to claim 6 is characterized in that: Step 4 specifically includes: 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: 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; Leveraging Datasets Train GNet using the dataset Validation is performed during training.

8. The gas turbine wheel disc shape optimization design method based on Bayesian optimization and GCN according to claim 7 is characterized in that: Based on the predicted stress field, the stress concentration phenomenon in the key parts of the wheel disc structure is monitored and identified as follows: Where, σ loc,max is the maximum local stress at the key part of the structure; σ loc,m is the average value of the local stress; σ th is the stress threshold for stress concentration monitoring; K is the local structural stress concentration factor; First, the stress threshold σ is determined based on the gas turbine wheel material and the working conditions of high temperature, high temperature gradient and high speed. th Secondly, based on the predicted stress field, the stress values of key parts of the wheel structure are monitored. If the maximum stress value σ loc,max Exceed σ th , then it is necessary to judge the degree of stress concentration; finally, by σ loc,max and σ loc,m Calculate the local structural stress concentration factor K to characterize the degree of stress concentration in the key part.

9. The gas turbine wheel disc shape optimization design method based on Bayesian optimization and GCN according to claim 7 is characterized in that: Step 5 specifically includes: 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. The gas turbine wheel disc shape optimization design method based on Bayesian optimization and GCN according to claim 9, 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 (EI) widely used in standard Bayesian optimization. It has good robustness, making it easier for the Bayesian optimization process to obtain the global optimal solution. 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 the midpoint in the unstable region; f(x) is the function from Gaussian process regression; x + =argmaxf(x i ).

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