A turbine wheel profile optimization method based on WGAN

Abstract

The application discloses a turbine wheel profile optimization method based on WGAN, comprising the following steps: S1, constructing a parameterized model of a turbine wheel; S2, generating a wheel structure sample; S3, data preprocessing; S4, constructing a physical field prediction model based on a Graph-Based CNN; S5, constructing a wheel shape generation model based on WGAN; and S6, performing multi-objective optimization on the wheel by using a gradient descent method. The turbine wheel profile optimization method based on WGAN has wide applicability to turbine wheels, greatly improves the efficiency and optimization effect of turbine wheel design optimization, and has the advantages of high optimization efficiency, wide optimization range, continuous design variables, strong interpretability and the like.

Description

Technical Field

[0001] This invention belongs to the field of turbine machinery structure optimization, specifically relating to a method for optimizing the turbine machinery wheel profile based on WGAN. Background Technology

[0002] The rotor disc is one of the key components of turbine machinery, and its performance directly affects the operation of the entire equipment. By optimizing the structural design of the turbine machinery rotor disc, its strength and vibration characteristics can be improved, while its weight and material costs can be reduced, thereby increasing the reliability of the turbine machinery and extending its service life. Therefore, the comprehensive design optimization of the turbine machinery rotor disc structure is of great significance for improving turbine machinery performance and reducing manufacturing costs.

[0003] In the optimization of turbine disk structures, traditional design methods typically employ heuristic optimization approaches, which have the following shortcomings:

[0004] 1) Optimization methods based on heuristic algorithms require a lot of computing resources to calculate the target variable, parameter tuning takes a long time, is sensitive to the initial design, converges slowly, and has high computational cost.

[0005] 2) Optimization methods based on traditional surrogate models lose information about the physical field during the optimization process and have high requirements for the sampling pass rate, thus limiting the range of the algorithm to search for the optimal solution.

[0006] 3) As design parameters increase, the cost of manual design increases, and the range of manually set design space is too small, often smaller than the real and complete optimization space, thus losing the meaning of optimization.

[0007] Therefore, establishing a fast and accurate roulette physics prediction model and a multi-objective optimization method for roulette to improve the efficiency of roulette design and optimization is an urgent problem to be solved. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the present invention aims to provide a WGAN-based method for optimizing the profile of turbine wheel disks, thereby solving one or more of the aforementioned technical problems. The technical solution provided by this invention has advantages such as high optimization efficiency, a wide optimization range, continuous design variables, and strong interpretability.

[0009] The present invention is achieved using the following technical solution:

[0010] A method for optimizing the turbine disk profile based on WGAN includes the following steps:

[0011] S1: Constructing a parametric model of the turbine's mechanical disk:

[0012] For the turbine disk structure, a parametric representation of the disk profile is achieved, and the profile parameter S is determined. i The corresponding design space Ω uses a parametric design method to represent different shaped disks, where i = 1, 2, 3, ..., n, and n is the number of disk profile parameters;

[0013] S2: Generating wheel structure samples:

[0014] Within the roulette wheel design parameter space Ω, design parameters are randomly sampled to form a design parameter sample set. Then, a corresponding roulette wheel shape dataset is generated based on the sampled design parameter sample set. Design variable samples that cannot form a closed roulette wheel model are verified and removed from the sample set, resulting in a design parameter sample set consisting of p design parameter samples that satisfy the constraints. Wherein, a single design parameter sample is denoted as And obtain a wheel shape dataset consisting of wheel shape data samples that correspond one-to-one with p design parameter samples. Wherein, a single shape data sample is denoted as The boundary conditions of the roulette wheel model are determined based on actual working conditions, and the boundary conditions are kept constant. A parametric design language is used to process the design parameter sample set. The data is used as input for finite element analysis to obtain the physical field information dataset corresponding to each design parameter sample. in, This is a dataset of sample physical fields; Optimize the target parameter set for the sample;

[0015] S3: Data Preprocessing

[0016] The physical field information dataset obtained in step S2 Filter the calculated data from After removing design parameter samples that do not meet the stress requirements and those with calculation abnormalities, the filtered design parameter sample set, roulette shape dataset, and physics field information dataset are respectively... and The physical field information calculated by the finite element method is then preprocessed to make the output of the physical field conform to the input format of the physical field prediction model.

[0017] S4: Construct a physics prediction model based on Graph-Based CNN:

[0018] Build and train a Graph-Based CNN physics prediction model to achieve prediction from a set of design parameters. Roulette Shape Dataset To the physical field information dataset Mapping between;

[0019] S5: Construct a roulette wheel shape generation model based on WGAN:

[0020] Construct and train a WGAN generative adversarial network to learn the generation and discrimination methods of roulette wheel shapes, and realize a continuous mapping from sampling to roulette wheel shape data;

[0021] S6: Multi-objective optimization of the roulette wheel using gradient descent:

[0022] The WGAN roulette shape generation model is used to quickly obtain roulette shape data, and then a Graph-Based CNN physics prediction model is used to predict the physics field and target parameter values. Gradient descent is used to predict the design variable S. i Optimize to obtain the design parameter values ​​with the best overall performance.

[0023] A further improvement of the present invention is that the implementation method of step S1 is as follows:

[0024] 101) Determine the wheel profile parameter S i ;

[0025] 102) Determine the design space Ω for the wheel profile parameters; profile parameters S i The following constraint equations must be satisfied:

[0026] b i,min ≤S i ≤b i,max

[0027] Among them, b i,min and b i,max The parameters S of the wheel profile are respectively i The lower and upper bounds.

[0028] A further improvement of the present invention is that, in step S2, the Latin hypercube sampling method is used to randomly sample the design parameters within the roulette wheel design parameter space Ω.

[0029] A further improvement of the present invention is that, in step S2, the physical field information dataset... The format is:

[0030]

[0031] Where a represents the node number, x, y, z represent the coordinates of the node in the three directions, and f represents the value of the node's state variable.

[0032] A further improvement of the present invention is that the implementation method of step S4 is as follows:

[0033] 401) Build a Graph-Based CNN physics prediction model. The Graph-Based CNN physics prediction model will use the roulette wheel shape data... Use it as input for training;

[0034] The mapping relationship between the design parameter x of the roulette wheel and the physical field is written as follows:

[0035]

[0036] Where: x represents the design parameters of the roulette wheel, converted into the corresponding roulette wheel shape data. This is then used as input to the Graph-BasedCNN physics prediction model; Θ represents the parameters to be learned by the model. This represents the mapping relationship between inputs and outputs; For the predicted physical field; The target parameters for prediction;

[0037] 402) Determine the optimization objective function of the network architecture. Its expression is:

[0038]

[0039] Where: B is the batch size; Num is the number of data nodes participating in training; w1 and w2 are the weights of the loss function; a is the true optimization target parameter; r is the true physical field;

[0040] 403) Network prediction performance evaluation metrics; For physics prediction, the mean absolute deviation (MEAE) and maximum absolute deviation (MAAE) are used as evaluation metrics to measure prediction performance, and their expressions are as follows:

[0041]

[0042]

[0043] Where: Num r r is the total number of nodes in the physical field. max and r min These represent the maximum and minimum values ​​of the real physical field;

[0044] For optimizing the prediction of the target variable, the coefficient of determination (R² score) is also used to measure the accuracy of the prediction, defined as:

[0045]

[0046] in: To truly optimize the mean of the target parameters;

[0047] 404) Network training; Based on the sample data preprocessed in step S3, the Adam algorithm is used to train the model, and multiple training stages are set. In each stage, the learning rate is set to 0.1 times that of the previous stage.

[0048] A further improvement of the present invention is that the implementation method of step S5 is as follows:

[0049] 501) Construct a WGAN generative adversarial network; adopt WGAN-GP as the basic architecture, and introduce Wasserstein distance to replace the JS divergence in the original GAN ​​to measure the difference between generated data and real data;

[0050] 502) Train the WGAN model to achieve a continuous mapping from sampling to roulette shape data.

[0051] A further improvement of this invention is that a roulette wheel shape is generated from an abstract sampling space using a generative network, and then the generated roulette wheel shape is mixed into the real roulette wheel shape dataset containing a large amount of roulette wheel shape data obtained in step S3. In this model, a discriminant network is used to distinguish between generated and real shapes. The generator network learns continuously to generate more realistic data to deceive the discriminant network, while the discriminant network also learns continuously to improve its ability to distinguish between real and fake data, until a Nash equilibrium is reached, that is, when the data generated by the generator network is realistic enough that the discriminant network cannot distinguish between generated and real shapes, the model training is complete.

[0052] A further improvement of this invention is that the optimization objective of WGAN-GP is expressed as:

[0053]

[0054] in, D represents the expected value of the distribution P specified in the subscript. w For the discriminator, the optimized parameter is w, and G θ The generator is defined by parameter θ; z is a random distribution. Let be the gradient with respect to variable x; β is the weight of the gradient penalty loss term; It is a weighted average of real data and generated data, specifically in the form of:

[0055]

[0056] Where: ε is the weight of the mixture of real data and generated data;

[0057] The generator and discriminator are trained using the Adam optimizer, and the training of the generator and discriminator is carried out alternately. The MMD method is used as an evaluation index for the similarity between the generator's generated data distribution and the real data distribution. The smaller the MMD value, the more similar the two distributions are, and the more difficult it is for the discriminator to distinguish them. The EOG algorithm is used as an evaluation index for the quality of the generated data itself. EOG is used as an index to evaluate the clarity of the generated data by accumulating the gradient values ​​of all nodes.

[0058] A further improvement of the present invention is that the implementation method of step S6 is as follows:

[0059] 601) Select the optimization objective f opt The mathematical description of roulette wheel profile optimization is as follows:

[0060] Optimization goal:

[0061] Constraints: stg j (x)<0,j=1,2,…J

[0062] h k (x) < 0, k = 1, 2, ..., K

[0063] in: To predict the optimization target parameters, the physics prediction model based on Graph-Based CNN constructed in step S4 establishes a direct mapping relationship between the roulette wheel design parameters and the optimization target variables. Its expression is: x is the input to the physics prediction model, and here it represents the design variable {S} of the roulette wheel. i};w i The weights corresponding to each optimization objective parameter; g j and h k For constraint functions;

[0064] 602) Based on the WGAN roulette shape generation model constructed in step S5, the roulette shape data is quickly obtained, and then the Graph-Based CNN physics prediction model constructed in step S4 is used to predict the physics field and target parameter values.

[0065] 603) The gradient-based automatic differentiation mechanism optimizes variable x in the following way:

[0066]

[0067] Where: x opt The design variable is the optimized value; τ is the step size factor for controlling the update. To optimize the gradient of the objective.

[0068] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0069] This invention provides a method for optimizing the profile of a turbine disk based on WGAN, which has wide applicability to turbine disks and greatly improves the efficiency and effect of turbine disk design optimization. It has the advantages of high optimization efficiency, wide optimization range, continuous design variables, and strong interpretability.

[0070] Furthermore, this invention establishes a Graph-Based CNN physics prediction model that uses roulette wheel shape data as input, eliminating the need to mesh the roulette wheel before inputting it into the model, thus saving prediction time and enabling rapid prediction of both optimized target variables and high-precision physics fields simultaneously.

[0071] Furthermore, this invention efficiently obtains roulette shape samples by establishing a roulette shape generation model based on WGAN. This model uses abstract design features to replace roulette design variables to generate roulette shapes, thereby making the design variables continuously differentiable and expanding the optimization space of the roulette profile.

[0072] Furthermore, based on the automatic differentiation mechanism, this invention considers the optimization target weights and combines WGAN and Graph-BasedCNN physics prediction models to establish a multi-objective gradient descent optimization method for the roulette wheel. This method can achieve comprehensive optimization of the roulette wheel profile without manual intervention or finite element analysis, and can automatically obtain a large number of roulette wheel profile design schemes and roulette wheel physics distribution, thereby significantly improving optimization efficiency. Attached Figure Description

[0073] Figure 1 This is a flowchart of a turbine wheel profile optimization method based on WGAN according to the present invention.

[0074] Figure 2 This is a schematic diagram of the structure and parameter settings of the gas turbine disk in an embodiment of the present invention.

[0075] Figure 3 This is a schematic diagram of the Graph-Based CNN physics prediction model structure in this invention.

[0076] Figure 4 This is a schematic diagram of the WGAN model structure in this invention. Detailed Implementation

[0077] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0078] Please see Figure 1 As shown, the present invention provides a method for optimizing the turbine disk profile based on WGAN, comprising the following steps:

[0079] S1: Constructing a parametric model of the turbine's mechanical disk:

[0080] For the turbine disk structure, a parametric representation of the disk profile is achieved, and the profile parameter S is determined. i The corresponding design space Ω uses a parametric design method to represent different shaped disks, where i = 1, 2, 3, ..., n, and n is the number of disk profile parameters.

[0081] Specifically, step S1 is implemented as follows:

[0082] 101) Determine the wheel profile parameter S i In this embodiment, a gas turbine disk is used as an example. The geometry of the upper half of the teeth on the end face of the disk is fixed because these structures may have structural coupling relationships with the blades, cylinders, and adjacent disks. The design scheme of the turbine disk is described by the inner diameter R1 of the disk, the lengths of each straight segment L1 to L7, the radius of the arc of the transition segment R2 to R5, and the angles θ1 to θ2. For the specific meaning of each parameter, please refer to [reference needed]. Figure 2 .

[0083] 102) Determine the design space Ω for the wheel profile parameters. Profile parameters S i The following constraint equations must be satisfied:

[0084] b i,min ≤S i ≤b i,max

[0085] Among them, b i,min and b i,max The parameters S of the wheel profile are respectively i The lower and upper bounds.

[0086] Due to geometric constraints—ensuring the roulette wheel's shape is closed—the parameters are not absolutely independent; preceding parameters affect the effective value range of subsequent parameters. If each parameter is sampled only within its own independent range, the sampling pass rate will be very low. Therefore, a dynamic adjustment of the design space based on constraints should be adopted. The value range of subsequent parameters should be dynamically adjusted according to the constraints determined by the preceding parameters to form a new effective design space.

[0087] S2: Generating wheel structure samples:

[0088] The Latin hypercube sampling (LHS) method is used to randomly sample design parameters within the roulette wheel design parameter space Ω, forming a design parameter sample set. Then, a corresponding roulette wheel shape dataset is generated based on the sampled design parameter data set. Design variable samples that cannot form a closed roulette wheel model are then checked and removed from the sample set, resulting in a design parameter sample set consisting of p design parameter samples that satisfy the constraints. Wherein, a single design parameter sample is denoted as And obtain a wheel shape dataset consisting of wheel shape data samples that correspond one-to-one with p design parameter samples. Wherein, a single shape data sample is denoted as The boundary conditions of the roulette wheel model are determined based on actual working conditions, and the boundary conditions are kept constant. A parametric design language is used to process the design parameter sample set. The data is used as input for finite element analysis to obtain the physical field information dataset corresponding to each design parameter sample. in, The dataset consists of physical field data for the samples, including temperature field data, stress field data, etc. The target parameter set for the sample is optimized, including maximum radial stress, maximum equivalent stress, and maximum radial displacement.

[0089] Specifically, physical field information dataset The format is:

[0090]

[0091] Where a represents the node number, x, y, z represent the coordinates of the node in the three directions, and f represents the value of the node's state variables, such as temperature, equivalent stress, etc.

[0092] S3: Data Preprocessing

[0093] The physical field information dataset obtained in step S2 Filter the calculated data from After removing design parameter samples that do not meet the stress requirements and those with calculation abnormalities, the filtered design parameter sample set, roulette shape dataset, and physics field information dataset are respectively... and The physical field information calculated by the finite element method is then preprocessed to ensure that the output of the physical field conforms to the input format of the physical field prediction model.

[0094] S4: Construct a physics prediction model based on Graph-Based CNN:

[0095] Build and train a Graph-Based CNN physics prediction model to achieve prediction from a set of design parameters. Roulette Shape Dataset To the physical field information dataset The mapping between them.

[0096] Specifically, step S4 is implemented as follows:

[0097] 401) Build a Graph-Based CNN physics prediction model. Graph-Based CNN does not use the design parameters of the roulette wheel as input to the network, but instead uses the shape data of the roulette wheel. Learning is performed using the input. The structure of the Graph-Based CNN physics prediction model is as follows: Figure 3 As shown, the top left is a shape feature learning structure combining convolutional and pooling layers, learning high-level features from the wheel shape; the right side of the network is a combination of fully connected layers used to predict and optimize target parameters; the bottom of the network is a physics prediction network formed by a combination of convolution and upsampling, used to reconstruct the physics field of the wheel. Once trained, there is no need to discretize the wheel structure into grid cells during the usage phase, thus saving prediction time.

[0098] The mapping relationship between the design parameter x of the roulette wheel and the physical field can be written as:

[0099]

[0100] Where: x represents the design parameters of the roulette wheel, converted into the corresponding roulette wheel shape data. This is then used as input to the Graph-BasedCNN physics prediction model; Θ represents the parameters to be learned by the model. This represents the mapping relationship between inputs and outputs; For the predicted physical field; These are the predicted optimization target parameters.

[0101] 402) Determine the optimization objective function of the network architecture. Its expression is:

[0102]

[0103] Where: B is the batch size; Num is the number of data nodes participating in training; w1 and w2 are the weights of the loss function; a is the true optimization target parameter; and r is the true physical field.

[0104] 403) Network Prediction Performance Evaluation Indicators. For physics field prediction, the Mean Absolute Deviation (MEAE) and Maximum Absolute Deviation (MAAE) are used as evaluation indicators to measure prediction performance. MEAE describes the average level of prediction performance across the entire physics field, while MAAE describes the maximum prediction deviation value across the entire physics field. MAAE directly reflects key physical quantities such as maximum stress and maximum displacement from the finite element analysis results. Its expression is:

[0105]

[0106]

[0107] Where: Num r r is the total number of nodes in the physical field. max and r min These represent the maximum and minimum values ​​of the real physical field.

[0108] For optimizing the prediction of the target variable, in addition to MEAE, the evaluation metric also uses the coefficient of determination (R²) to measure the accuracy of the prediction, defined as:

[0109]

[0110] in: To truly optimize the mean of the target parameters.

[0111] 404) Network Training. Based on the sample data preprocessed in step S3, the Adam algorithm is used to train the model. Multiple training stages are set, and the learning rate in each stage is set to 0.1 times that of the previous stage. This helps to prevent model overfitting and improve training performance.

[0112] S5: Construct a roulette wheel shape generation model based on WGAN:

[0113] We construct and train a WGAN generative adversarial network to learn how to generate and distinguish roulette wheel shapes, thus achieving a continuous mapping from sampling to roulette wheel shape data.

[0114] Specifically, step S5 is implemented as follows:

[0115] 501) Constructing a WGAN generative adversarial network. In this embodiment, WGAN-GP (Wasserstein GAN with gradient penalty) is used as the basic architecture. The Wasserstein distance is introduced to replace the JS divergence in the original GAN ​​to measure the difference between generated and real data. The structure of the WGAN generative adversarial network is as follows: Figure 4 As shown, the activation function between the network convolutional layers is the LeakyReLU function, which retains a certain activation value when the input is negative. This means that the LeakyReLU function can process more information, thereby improving the model's performance and reducing overfitting.

[0116] 502) Train the WGAN model to achieve a continuous mapping from sampling to roulette wheel shape data. Generate roulette wheel shapes from an abstract sampling space using a generative network, and then mix the generated roulette wheel shapes into the real roulette wheel shape dataset obtained in step S3, which contains a large amount of roulette wheel shape data. In this model, a discriminant network is used to distinguish between generated and real shapes. The generator network continuously learns and generates more realistic data to deceive the discriminant network, while the discriminant network also continuously learns to improve its ability to distinguish between real and fake data. This creates a dynamic game between the two, causing the generator network to continuously improve and generate more realistic roulette shape data until a Nash equilibrium is reached—that is, when the data generated by the generator network is realistic enough that the discriminant network can no longer distinguish between generated and real shapes, at which point model training is complete.

[0117] The optimization objective of WGAN-GP can be expressed as:

[0118]

[0119] in, D represents the expected value of the distribution P specified in the subscript. w For the discriminator, the optimized parameter is w, and G θ The generator is defined by parameter θ; z is a random distribution. Let be the gradient with respect to variable x; β is the weight of the gradient penalty loss term; It is a weighted average of real data and generated data, specifically in the form of:

[0120]

[0121] Where: ε is the weight of the mixture of real data and generated data.

[0122] In this embodiment, the generator and discriminator are trained using the Adam optimizer, and the training of the generator and discriminator is performed alternately. The Maximum Mean Discrepancy (MMD) method is used as an evaluation metric for the similarity between the generator's generated data distribution and the real data distribution. The smaller the MMD value, the more similar the two distributions are, and the more difficult it is for the discriminator to distinguish them. The Energy of Gradient (EOG) algorithm is used as an evaluation metric for the quality of the generated data itself. EOG accumulates the gradient values ​​of all nodes and is used as an indicator to assess the clarity of the generated data.

[0123] S6: Multi-objective optimization of the roulette wheel using gradient descent:

[0124] The WGAN roulette shape generation model is used to quickly obtain roulette shape data, and then a Graph-Based CNN physics prediction model is used to predict the physics field and target parameter values. Gradient descent is used to predict the design variable S. i Optimize to obtain the design parameter values ​​with the best overall performance.

[0125] Specifically, step S6 is implemented as follows:

[0126] 601) Select the optimization objective f opt The mathematical description of roulette wheel profile optimization is as follows:

[0127] Optimization goal:

[0128] Constraints: stg j (x) < 0, j = 1, 2, ..., J

[0129] h k (x)<0,k=1,2,…K

[0130] in: The predicted optimization target parameters may include maximum equivalent stress, maximum radial stress, wheel weight, radial displacement, and response. The physics prediction model based on a graph-based CNN, constructed in step S4, establishes a direct mapping relationship between the wheel design parameters and the optimization target variables. Its expression is: x is the input to the physics prediction model, and here it represents the design variable {S} of the roulette wheel. i};w i The weights corresponding to each optimization objective parameter; g j and h k For constraint functions.

[0131] 602) Based on the WGAN roulette shape generation model constructed in step S5, the roulette shape data is quickly obtained, and then the Graph-Based CNN physics prediction model constructed in step S4 is used to predict the physics field and target parameter values.

[0132] 603) The gradient-based automatic differentiation mechanism optimizes variable x in the following way:

[0133]

[0134] Where: x opt The design variable is the optimized value; τ is the step size factor for controlling the update. To optimize the gradient of the objective.

[0135] When using the gradient descent method to complete the iterative process, the optimal design parameter values ​​for the turbine disk with the best comprehensive index are obtained. In engineering applications, different weight coefficients for the optimization objective variables can be set according to actual needs, and different optimization objective functions can be selected, thereby quickly obtaining the optimal disk profile of the turbine disk under a certain working condition based on the above framework.

[0136] In this embodiment, the established Graph-Based CNN physics prediction model uses roulette wheel shape data as input without requiring meshing of the roulette wheel before inputting it into the model. Compared with traditional surrogate models that lose physics information during optimization, this model can simultaneously achieve rapid prediction of both the target variable and the high-precision physics, and significantly saves prediction time. A roulette wheel shape generation model based on WGAN is established to efficiently obtain roulette wheel shape samples. Abstract design features are used to replace roulette wheel design variables to generate roulette wheel shapes, thus making the design variables continuously differentiable. At the same time, compared with manually setting the design space range, which has a low sampling success rate, the optimization space of the roulette wheel shape is significantly widened, allowing the algorithm to search for the optimal solution in a wider range. Based on the characteristic of continuously differentiable design variables of the WGAN generation model, a multi-objective gradient descent optimization method for roulette wheels is used to complete the comprehensive optimization of the roulette wheel shape. Compared with heuristic optimization methods that are sensitive to the initial design, have slow convergence, and high computational cost, this method can significantly improve optimization efficiency.

[0137] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A method for optimizing the turbine wheel profile based on WGAN, characterized in that, Includes the following steps: S1: Constructing a parametric model of the turbine's mechanical disk: For the turbine disk structure, a parametric representation of the disk profile is achieved, and the profile parameter S is determined. i The corresponding design space Ω uses a parametric design method to represent different shaped disks, where i = 1, 2, 3, ..., n, and n is the number of disk profile parameters; S2: Generating wheel structure samples: Within the roulette wheel design parameter space Ω, design parameters are randomly sampled to form a design parameter sample set. Then, a corresponding roulette wheel shape dataset is generated based on the sampled design parameter sample set. Design variable samples that cannot form a closed roulette wheel model are verified and removed from the sample set, resulting in a design parameter sample set consisting of p design parameter samples that satisfy the constraints. Wherein, a single design parameter sample is denoted as And obtain a wheel shape dataset consisting of wheel shape data samples that correspond one-to-one with p design parameter samples. Wherein, a single shape data sample is denoted as The boundary conditions of the roulette wheel model are determined based on actual working conditions, and the boundary conditions are kept constant. A parametric design language is used to process the design parameter sample set. The data is used as input for finite element analysis to obtain the physical field information dataset corresponding to each design parameter sample. in, This is a dataset of sample physical fields; Optimize the target parameter set for the sample; S3: Data Preprocessing The physical field information dataset obtained in step S2 Filter the calculated data from After removing design parameter samples that do not meet the stress requirements and those with calculation abnormalities, the filtered design parameter sample set, roulette shape dataset, and physics field information dataset are respectively... and The physical field information calculated by the finite element method is then preprocessed to make the output of the physical field conform to the input format of the physical field prediction model. S4: Construct a physics prediction model based on Graph-Based CNN: Build and train a Graph-Based CNN physics prediction model to achieve prediction from a set of design parameters. Roulette Shape Dataset To the physical field information dataset Mapping between; S5: Construct a roulette wheel shape generation model based on WGAN: Construct and train a WGAN generative adversarial network to learn the generation and discrimination methods of roulette wheel shapes, and realize a continuous mapping from sampling to roulette wheel shape data; S6: Multi-objective optimization of the roulette wheel using gradient descent: The WGAN roulette shape generation model is used to quickly obtain roulette shape data, and then a Graph-Based CNN physics prediction model is used to predict the physics field and target parameter values. Gradient descent is used to predict the design variable S. i Optimize to obtain the design parameter values ​​with the best overall performance.

2. The method for optimizing the turbine wheel profile based on WGAN according to claim 1, characterized in that, The implementation method for step S1 is as follows: 101) Determine the wheel profile parameter S i ; 102) Determine the design space Ω for the wheel profile parameters; profile parameters S i The following constraint equations must be satisfied: b i，min ≤S i ≤b i，max Among them, b i,min and b i,max The parameters S of the wheel profile are respectively i The lower and upper bounds.

3. The method for optimizing the turbine wheel profile based on WGAN according to claim 1, characterized in that, In step S2, the Latin hypercube sampling method is used to randomly sample the design parameters within the roulette wheel design parameter space Ω.

4. The method for optimizing the turbine wheel profile based on WGAN according to claim 1, characterized in that, In step S2, the physical field information dataset The format is: Where a represents the node number, x, y, z represent the coordinates of the node in the three directions, and f represents the value of the node's state variable.

5. The method for optimizing the turbine wheel profile based on WGAN according to claim 1, characterized in that, The implementation method for step S4 is as follows: 401) Build a Graph-Based CNN physics prediction model. The Graph-Based CNN physics prediction model will use the roulette wheel shape data... Use it as input for training; The mapping relationship between the design parameter x of the roulette wheel and the physical field is written as follows: Where: x represents the design parameters of the roulette wheel, converted into the corresponding roulette wheel shape data. This is then used as input to the Graph-Based CNN physics prediction model; Θ represents the parameters to be learned by the model. This represents the mapping relationship between inputs and outputs; For the predicted physical field; The target parameters for prediction; 402) Determine the optimization objective function of the network architecture. Its expression is: Where: B is the batch size; Num is the number of data nodes participating in training; w1 and w2 are the weights of the loss function; a is the true optimization target parameter; r is the true physical field; 403) Network prediction performance evaluation metrics; For physics prediction, the mean absolute deviation (MEAE) and maximum absolute deviation (MAAE) are used as evaluation metrics to measure prediction performance, and their expressions are as follows: Where: Num r r is the total number of nodes in the physical field. max and r min These represent the maximum and minimum values ​​of the real physical field; For optimizing the prediction of the target variable, the coefficient of determination (R² score) is also used to measure the accuracy of the prediction, defined as: in: To truly optimize the mean of the target parameters; 404) Network training; Based on the sample data preprocessed in step S3, the Adam algorithm is used to train the model, and multiple training stages are set. In each stage, the learning rate is set to 0.1 times that of the previous stage.

6. The method for optimizing the turbine wheel profile based on WGAN according to claim 1, characterized in that, The implementation method for step S5 is as follows: 501) Construct a WGAN generative adversarial network; adopt WGAN-GP as the basic architecture, and introduce Wasserstein distance to replace the JS divergence in the original GAN ​​to measure the difference between generated data and real data; 502) Train the WGAN model to achieve a continuous mapping from sampling to roulette shape data.

7. The method for optimizing the turbine wheel profile based on WGAN according to claim 6, characterized in that, A generative network generates wheel shapes from an abstract sampling space, and then the generated wheel shapes are mixed into the real wheel shape dataset obtained in step S3, which contains a large amount of wheel shape data. In this process, a discriminant network is used to distinguish between the generated shape and the real shape; The generative network learns continuously to generate more realistic data to deceive the discriminative network, while the discriminative network also learns continuously to improve its ability to distinguish between real and fake data, until the Nash equilibrium is reached, that is, when the data generated by the generative network is realistic enough that the discriminative network cannot distinguish between generated shapes and real shapes, the model training is complete.

8. The method for optimizing the turbine wheel profile based on WGAN according to claim 6, characterized in that, The optimization objective of WGAN-GP is expressed as: in, D represents the expected value of the distribution P specified in the subscript; w For the discriminator, the optimized parameter is w, and G θ The generator is defined by parameter θ; z is a random distribution. Let be the gradient with respect to variable x; β is the weight of the gradient penalty loss term; It is a weighted average of real data and generated data, specifically in the form of: Where: ε is the weight of the mixture of real data and generated data; The generator and discriminator are trained using the Adam optimizer, and the training of the generator and discriminator is carried out alternately. The MMD method is used as an evaluation index for the similarity between the generator's generated data distribution and the real data distribution. The smaller the MMD value, the more similar the two distributions are, and the more difficult it is for the discriminator to distinguish them. The EOG algorithm is used as an evaluation index for the quality of the generated data itself. EOG is used as an index to evaluate the clarity of the generated data by accumulating the gradient values ​​of all nodes.

9. The method for optimizing the turbine wheel profile based on WGAN according to claim 1, characterized in that, The implementation method for step S6 is as follows: 601) Select the optimization objective f opt The mathematical description of roulette wheel profile optimization is as follows: Optimization goal: Constraints: stg j (x) < 0, j = 1, 2, ..., J h k (x)<0,k=1,2,…K in: To predict the optimization target parameters, the physics prediction model based on Graph-Based CNN constructed in step S4 establishes a direct mapping relationship between the roulette wheel design parameters and the optimization target variables. Its expression is: x is the input to the physics prediction model, and here it represents the design variable {S} of the roulette wheel. i };w i The weights corresponding to each optimization objective parameter; g j and h k For constraint functions; 602) Based on the WGAN roulette shape generation model constructed in step S5, the roulette shape data is quickly obtained, and then the Graph-Based CNN physics prediction model constructed in step S4 is used to predict the physics field and target parameter values. 603) The gradient-based automatic differentiation mechanism optimizes variable x in the following way: Where: x opt The design variable is the optimized value; τ is the step size factor for controlling the update. To optimize the gradient of the objective.

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