A method for predicting two-dimensional irregular flow fields in turbine stages based on SuperDeepONet neural network

Abstract

This invention discloses a method for predicting two-dimensional irregular flow fields in turbine stages based on the SuperDeepONet neural network, comprising the following steps: constructing a parameterized turbine stage geometric model and generating a sample dataset; establishing a SuperDeepONet neural network model, which, based on the DeepONet architecture, introduces a signed distance field as an additional input to the backbone network to enhance the perception of irregular geometric boundaries; constructing a dual-backbone network structure to process dynamic and static blade data separately, and introducing a three-stage data fusion mechanism in the middle of the network to achieve effective coupling and full information interaction between the dynamic and static blade flow fields; and training and optimizing the SuperDeepONet model using the sample dataset. According to this invention, it is possible to quickly and accurately predict the internal flow field of turbine stages with irregular boundaries and geometrically variable characteristics.

Description

Technical Field

[0001] This invention relates to the technical field of the intersection of computational fluid dynamics (CFD) and artificial intelligence (AI), and in particular to a method for predicting two-dimensional irregular flow fields in turbine stages based on the SuperDeepONet neural network. Background Technology

[0002] Turbines, compressors, and other turbomachinery are core components in energy, aerospace, and other fields, and their performance optimization depends on the accurate prediction of their complex internal flow fields. Traditional experimental measurement methods are costly and time-consuming. Although computational fluid dynamics (CFD) methods have become the mainstream analysis tool, they consume huge amounts of computational resources and are inefficient in processes such as turbine design optimization that require a large number of iterative calculations.

[0003] To reduce the computational cost of CFD, surrogate models (such as Kriging models, support vector machines, and neural networks) have been introduced. However, turbine internal flow fields are characterized by ultra-high dimensionality and strong nonlinearity, and traditional surrogate models are mostly black-box models with poor generalization ability. In recent years, deep learning models, especially convolutional neural networks (CNNs), have been used as alternative models for CFD to achieve rapid flow field prediction. However, CNNs typically require input data with a regular grid structure (such as images), while the geometric boundaries of turbine internal flow channels are irregular, and CFD calculations are usually performed using unstructured grids with disordered node distribution. Pixelating unstructured grid data to accommodate CNNs can lead to problems such as loss of data precision, uneven information importance, and boundary coarsening.

[0004] The PointNet architecture can directly process point cloud data, avoiding the disadvantages of pixelation, and has been applied to some flow field prediction tasks. However, once PointNet is trained, the number of its input point clouds is fixed, which cannot adapt to flow field prediction with different numbers of nodes and geometric configurations, resulting in insufficient flexibility. DeepONet (Deep Operator Network), as a neural network framework for learning operators, has shown great potential in dealing with flow field prediction problems with varying geometry and number of nodes. However, existing DeepONet models have obvious limitations when applied to turbine flow field prediction: (1) Its backbone network usually only inputs the absolute coordinates (X, Y) of the nodes, lacking an explicit description of the geometric boundaries, resulting in insufficient perception of geometric changes. The same coordinate point may correspond to completely different physical states under different geometries (such as in the fluid domain or inside the blade body); (2) Most studies predict the flow fields of the stationary blade and the moving blade separately, failing to consider the coupling effect between the stationary and moving blades in the turbine stage; (3) The information interaction between its branch network and backbone network is only achieved through inner product in the last layer, and the data transmission is isolated from each other, which limits the learning ability and prediction accuracy of the model.

[0005] Therefore, there is an urgent need in this field for a novel neural network model and method that can directly process unstructured grid data, adapt to geometric changes, and accurately predict the overall flow field of a turbine stage. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the present invention aims to provide a method for predicting two-dimensional irregular flow fields in turbine stages based on the SuperDeepONet neural network. This method effectively solves the problems of high computational cost of traditional CFD methods, the inability of existing PointNet models to flexibly handle variable node numbers, and the poor adaptability and insufficient prediction accuracy of existing DeepONet models to geometric changes. The invention provides a SuperDeepONet neural network method and system capable of rapidly and accurately predicting two-dimensional flow fields in turbine stages with irregular boundaries and geometrically variable characteristics. To achieve the above-mentioned objectives and other advantages of the present invention, a method for predicting two-dimensional irregular flow fields in turbine stages based on the SuperDeepONet neural network is provided, comprising: A parameterized turbine stage geometric model was constructed and a sample dataset was generated. A SuperDeepONet neural network model was established, which, based on the DeepONet architecture, introduced a signed distance field (SDF) as an additional input to the backbone network to enhance the perception of irregular geometric boundaries. A dual-backbone network structure was constructed to process the dynamic and static blade data separately, and a three-stage data fusion mechanism was introduced in the middle of the network to achieve effective coupling and full information interaction between the dynamic and static blade flow fields. The SuperDeepONet model was trained and optimized using the sample dataset.

[0007] Compared with the prior art, the advantages and positive effects of the present invention are: (1) High-precision prediction: By introducing a signed distance field (SDF), the model can accurately perceive the spatial relationship between nodes and complex geometric boundaries, significantly improving its adaptability to geometric changes and the accuracy of flow field prediction. Experiments show that in the prediction tasks of pressure, temperature, and Mach number fields at multiple sections of the turbine stage, the SuperDeepONet model proposed in this invention significantly outperforms PointNet and the original DeepONet model. Compared with DeepONet, at the cost of only increasing training time by about 1 minute, the prediction error rate can be reduced by more than 60%, and the prediction error of most nodes can be controlled within 2%.

[0008] (2) Excellent flexibility: SuperDeepONet inherits the ability of DeepONet to handle the problem of variable number of nodes. It can predict unstructured grids with arbitrary node distribution, overcoming the limitation of the fixed number of input point clouds of the PointNet model.

[0009] (3) Effective coupling prediction: By constructing a dual-backbone network structure, the stationary and moving blade data are processed separately, and three data fusions are performed in the middle of the model, which realizes the full interaction and coupling prediction of the flow field information of the stationary and moving blades. This is more in line with the aero-thermodynamic coupling effect when the turbine stage is actually working, and improves the overall prediction accuracy.

[0010] (4) High efficiency: SuperDeepONet has high training and inference efficiency. Under the same hardware and more than 500 hidden layer neurons, its training time is only 1 / 10 to 1 / 100 of PointNet, which greatly saves computing resources and time costs.

[0011] (5) Strong robustness: The model can still maintain a high degree of consistency with the high-precision CFD simulation results in complex flow regions with drastic changes in physical field gradients, demonstrating excellent ability to capture local flow details and strong gradient changes, and the prediction results are stable and reliable.

[0012] In summary, this invention provides an innovative solution with high precision, high efficiency, and high flexibility for rapidly predicting the flow field in internal channels such as turbine stages, which have irregular boundaries and variable geometry. It has broad application prospects in the optimization design of turbomachinery. Attached Figure Description

[0013] Figure 1 A schematic diagram of the SuperDeepONet neural network model structure provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the arc parameterization in a turbine blade provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the parameterization of turbine blade thickness distribution provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the leading edge structure of a turbine blade provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of three-dimensional blade bending parameterization provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of three-dimensional blade torsion parameterization provided in an embodiment of the present invention; Figure 7 This is a schematic diagram of turbine meridional flow channel parameterization provided in an embodiment of the present invention; Figure 8 This is a schematic diagram of a turbine stage computational domain mesh provided in an embodiment of the present invention; Figure 9 This is a schematic diagram of the mesh independence verification results provided in an embodiment of the present invention; Figure 10 The prediction errors of three models under different epochs provided in this embodiment of the invention; Figure 11 The training time of three models under different epochs provided in this embodiment of the invention; Figure 12 This is a performance comparison chart of SuperDeepONet with different numbers of nodes provided in this embodiment of the invention; Figure 13 A comparison chart of training loss and validation loss for three models provided in embodiments of the present invention; Figure 14 A comprehensive comparison chart of prediction error and training time of the three models provided in the embodiments of the present invention on nine datasets; Figure 15 Histograms of prediction error distributions for three models provided in embodiments of the present invention; Figure 16 Comparison cloud diagrams of the predicted pressure fields of the turbine root, middle and top sections of the three models provided in the embodiments of the present invention with the CFD simulation results; Figure 17 Comparison cloud maps of the predicted temperature fields of the turbine root, middle and top sections of the three models provided in the embodiments of the present invention with the CFD simulation results; Figure 18 The image shows a comparison of the predicted Mach number fields at the root, middle, and top sections of the turbine stage using the three models provided in this embodiment of the invention, along with the CFD simulation results. (Detailed implementation details are provided.) The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0014] Reference Figure 1 A method for predicting two-dimensional irregular flow fields in turbine stages based on the SuperDeepONet neural network includes: Step 1: Turbine Stage Parameterization and Dataset Generation A parametric method based on Bezier and NURBS curves was employed to geometrically control the two-dimensional airfoils (including mid-curve, thickness distribution, leading and trailing edges), three-dimensional stacking (bending and torsion), and meridional channels of the turbine stator and rotor blades. Latin hypercube sampling (LHS) was used to generate 1500 different turbine stage geometric configuration samples within a defined parameter range. For each sample, high-fidelity CFD software (such as ANSYS CFX) was used to perform numerical simulations on a high-quality unstructured mesh to obtain pressure, temperature, and Mach number data for each node within the flow field. Simultaneously, the signed distance field (SDF) value to the nearest blade surface was calculated for each node. Finally, a large-scale dataset was constructed, containing input parameters (geometric parameters, node coordinates, node SDF values) and output targets (nodal flow field physical quantities).

[0015] Step 2: SuperDeepONet Model Construction The SuperDeepONet model proposed in this invention is a significant improvement on the traditional DeepONet architecture. Its core structure includes a branch network and two trunk networks.

[0016] Branch network: The input is a 104-dimensional parameterized vector representing the geometry of the entire turbine stage.

[0017] There are two backbone networks: a stationary blade backbone network and a moving blade backbone network. The input to each backbone network is the spatial parameters of the nodes within its corresponding flow field region (stationary blade domain or moving blade domain). These spatial parameters include the two-dimensional coordinates (X, Y) of the nodes and their corresponding signed distance field (SDF) values. Introducing SDF allows the model to explicitly perceive the relative positional relationship between the nodes and the geometric boundaries of the blades.

[0018] Data fusion mechanism: To address the issue of information isolation between the branch network and the backbone network, this invention introduces three data fusion operations in the middle of the model structure: After passing through the first hidden layer, the output features of the branch network are fused with the output features of the stationary leaf backbone network and the moving leaf backbone network in the first and second fusions, respectively. Subsequently, the features obtained from the first two fusions are fused a third time. The feature vectors obtained from these three fusions serve as inputs to the latter half of the stationary leaf backbone network, the latter half of the moving leaf backbone network, and the latter half of the branch network, respectively, achieving full interaction of information among the three network parts.

[0019] Output layer: The outputs of the latter half of the two backbone networks are merged and then combined with the outputs of the latter half of the branch networks through the Einstein Summation operation, finally outputting the predicted flow field physical quantities (pressure, temperature, Mach number) at each input node.

[0020] Step 3: Model Training and Hyperparameter Optimization The SuperDeepONet model was trained using the dataset generated in Step 1. To achieve optimal performance, a genetic algorithm was used to automatically optimize the model's key hyperparameters, primarily the learning rate and the number of hidden neurons. The genetic algorithm employed binary encoding, tournament selection, two-point crossover, and mutation operations. The training objective was to minimize the mean squared error (MSE) between the predicted values ​​and the CFD simulation values, and the Adam optimizer was selected.

[0021] Step 4: Flow Field Prediction For a new turbine stage design without CFD calculations, its geometric parameterization vector is first obtained. Then, the locations (coordinates) of the nodes to be predicted in the flow field regions of the stator and rotor blades are specified, and the SDF values ​​of these nodes are calculated. These parameters are then fed into a pre-trained SuperDeepONet model, which can output accurate pressure, temperature, and Mach number distributions at these nodes in seconds or even milliseconds.

[0022] 1. Data preparation (corresponding to step one) Parametricization: Using the parametricization method described in the manual, 104 control parameters are used to define the geometry of a single-stage turbine, including the airfoil profile, bending, stacking, and meridional flow channel of the stationary and moving blades.

[0023] Sampling: Using a certain benchmark turbine stage parameter as the initial value, within a reasonable parameter range determined after fluctuation and adjustment of ±5%, 1500 different parameter combinations were generated using the Latin hypercube sampling method.

[0024] CFD simulation: Steady flow simulation was performed for each sample using ANSYS CFX software. The SSTk-ω model was selected as the turbulence model, with an O+H hybrid grid of approximately 6 million cells (verified for grid independence). Boundary conditions were set as follows: inlet total temperature 1191.3 K, total pressure 451 kPa, outlet static pressure 98.3 kPa, and rotational speed 45000 rpm. After simulation convergence, the coordinates (X, Y) of the unstructured grid nodes within the flow field and their corresponding pressure (P), temperature (T), and Mach number (Ma) data were exported.

[0025] SDF calculation: For each node, calculate its Euclidean distance to the nearest blade surface (stationary or moving blade). The SDF value for that node is determined by whether it is located inside the fluid domain (positive sign) or outside (blade entity, negative sign).

[0026] Dataset Construction: The input for each sample includes a 104-dimensional geometric parameter vector, as well as the node coordinates and SDF values ​​sampled in the stationary and moving leaf domains respectively (e.g., 125 nodes sampled in each domain). The output is the pressure, temperature, and Mach number of the corresponding node. The 1500 samples are randomly divided into training, validation, and test sets in an 8:1:1 ratio.

[0027] 2. Model building and training (corresponding to steps two and three) Model Structure: The SuperDeepONet model is constructed using the PyTorch framework. The input dimension of the branch networks is 104, and the input dimension of the static / dynamic leaf backbone network is 3 (X coordinate, Y coordinate, SDF value). After the first hidden layer, three data fusions are performed using vector transformation. The output of the backbone network after merging is summed with the output of the branch networks using Einstein calculus to obtain the physics prediction contour map.

[0028] Hyperparameter optimization: A genetic algorithm is used to optimize the learning rate and the number of hidden layer neurons. Parameter range: learning rate (~), number of hidden layer neurons (50~1000). Genetic algorithm settings: binary encoding (6 bits per hyperparameter), population size set to 4, number of iterations set to 25, two-point crossover (probability 0.9), mutation (probability 0.01), tournament selection (size set to 4), fitness function is the average error of the test set.

[0029] Model Training: The model was trained on the training set using the optimized combination of hyperparameters. The iteration count was set to 1000, the batch size to 32, the loss function to MSE, and the optimizer to Adam. The training process was completed on a single NVIDIA GeForce RTX 5090 graphics card.

[0030] 3. Prediction and Evaluation (corresponding to step four) The trained SuperDeepONet model is evaluated on the test set and compared with PointNet and DeepONet models trained on the same dataset and with the same hyperparameter optimization process.

[0031] Quantitative indicators: For pressure and temperature fields, the mean relative error (MRE) of all nodes is calculated; for Mach number fields, since the relative error is distorted due to the small values ​​in some regions, the mean absolute error (MAE) is used.

[0032] Result: As Figures 14-18As shown, SuperDeepONet exhibits the lowest prediction error and the most concentrated low error distribution across all test scenarios. Its training time is significantly shorter than PointNet, approaching that of DeepONet, but with a significantly improved accuracy. Error contour plots show that SuperDeepONet can keep the error of most nodes within 2%, and maintains high accuracy even in regions with large gradient changes, while DeepONet exhibits larger errors in these areas.

[0033] Example 2: This example demonstrates a specific implementation of the system of the present invention. A turbine-stage two-dimensional irregular flow field prediction system based on the SuperDeepONet neural network includes: Parametric and Data Management Module: Provides a graphical or script interface, allowing users to define turbine parametric schemes, call parametric scripts to generate geometry, manage CFD simulation tasks and result data, and automatically calculate SDF.

[0034] Model building and training module: Provides a SuperDeepONet model template, allowing users to configure the number of network layers, activation functions, etc. It integrates a genetic algorithm optimizer for automatic hyperparameter optimization and model training.

[0035] Flow field prediction and visualization module: Users input new turbine parameters and the node coordinates to be predicted. The system automatically calls the trained model to make predictions and visualizes the results (such as pressure contour maps and error distributions).

[0036] The number of devices and processing scale described herein are for simplification of the invention. Applications, modifications, and variations of this invention will be readily apparent to those skilled in the art. Although embodiments of the invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for this invention, and further modifications can be readily implemented by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, this invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method for predicting two-dimensional irregular flow fields in turbine stages based on the SuperDeepONet neural network, characterized in that, Includes the following steps: S1. Construct the turbine stage geometric model, parameterize the turbine stage, and generate a sample dataset; S2. Establish the SuperDeepONet neural network model; S3. Train the SuperDeepONet neural network model using the sample dataset from step S1; S4. Input the parameterized vector of the turbine stage to be predicted, as well as the spatial parameters of the stationary and moving blade regions, into the SuperDeepONet neural network model trained in step S3. The model outputs the pressure, temperature, and Mach number flow field distribution of the turbine stage at the specified node.

2. The method for predicting two-dimensional irregular flow fields in turbine stages based on the SuperDeepONet neural network as described in claim 1, characterized in that, The SuperDeepONet neural network model includes a parameterized vector branch network for inputting the geometry of the turbine stage and two backbone networks; wherein, the two backbone networks are the stationary blade backbone network and the moving blade backbone network, respectively, for inputting the spatial parameters of the flow field regions of the stationary blade and the moving blade.

3. The method for predicting two-dimensional irregular flow fields in turbine stages based on the SuperDeepONet neural network as described in claim 2, characterized in that, The spatial parameters include the two-dimensional coordinates (X, Y) of the nodes and the signed distance field (SDF) data obtained through calculation.

4. The method for predicting two-dimensional irregular flow fields in turbine stages based on the SuperDeepONet neural network as described in claim 3, characterized in that, The SuperDeepONet neural network model performs three data fusion operations after the first hidden layer of the branch network and the two backbone networks, as follows: The first fusion performs a vector transformation between the branch network output and the static leaf backbone network output; The second fusion performs a vector transformation between the branch network output and the main stem network output; The third fusion transforms the results of the first two fusions into vectors; The fused results are fed back to the latter half of the two backbone networks and branch networks for further feature extraction. Finally, the outputs of the two main networks are merged and then summed with the outputs of the branch networks using Einstein's summation to obtain the flow field prediction results for the entire turbine stage.

5. The method for predicting two-dimensional irregular flow fields in turbine stages based on the SuperDeepONet neural network as described in claim 1, characterized in that, In step S3, a genetic algorithm is used to optimize the key hyperparameters of the model, including the learning rate and the number of neurons in the hidden layer. During training, mean squared error (MSE) is used as the loss function, and the Adam optimizer is used to update the model parameters.

6. The method for predicting two-dimensional irregular flow fields in turbine stages based on the SuperDeepONet neural network as described in claim 3, characterized in that, The signed distance field data is calculated as follows: for any node in the two-dimensional plane domain, calculate its Euclidean distance to the nearest blade surface, and assign a positive or negative sign to the distance value based on whether the node is located outside or inside the blade. The three data fusion operations are specifically as follows: Let the output of the first hidden layer of the branch network be... The output of the first hidden layer of the static leaf backbone network is The output of the first hidden layer of the moving leaf backbone network is ; The result of the first fusion was ; The result of the second fusion was The result of the third fusion was ;in, As input to subsequent layers of the static leaf backbone network As input to subsequent layers of the leaf-moving backbone network As input to subsequent layers of the branch network.

7. A turbine-stage two-dimensional irregular flow field prediction system based on a SuperDeepONet neural network for implementing the method of any one of claims 1-6, characterized in that, include: The parameterization and data generation module is used to perform turbine stage geometry parameterization and generate a training dataset containing CFD simulation results. The model building module is used to build the SuperDeepONet neural network model structure as described in claim 1; The model training and optimization module is used to train the SuperDeepONet model using the training dataset and optimize its hyperparameters using a genetic algorithm. The flow field prediction module is used to load the trained optimal model, receive new turbine stage parameters and spatial node information, and output the predicted flow field distribution.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1 to 6.

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