Blade meridian flow field prediction method based on explicit-implicit mechanism mining coding

Abstract

The invention discloses a blade meridian flow field prediction method based on explicit-implicit mechanism mining coding, and relates to the technical field of turbine blade design, the method comprises the following steps: obtaining meridian plane grids and design working condition parameters of a blade runner on an axial-flow compressor described by using a graph data structure; utilizing the trained blade meridian flow field prediction model to predict physical field data of each node of the meridian plane grid of the blade flow channel according to the meridian plane grid of the blade flow channel and the design working condition parameters; according to the method, the implicit mechanism mining mechanism is used for mining the implicit differential association relationship in the physical data as the data feature in the data feature extraction process of the graph neural network model, and the turbine flow analysis mechanism is explicitly encoded into the model loss function; based on the model loss function, a strategy for optimizing the blade meridian flow field prediction model through back propagation is trained, the blade meridian flow field prediction precision is improved, and the model generalization and the result confidence coefficient are improved.

Description

Technical Field

[0001] This application relates to the technical field of turbine blade design, and particularly to a method for predicting the meridional flow field of blades based on explicit and implicit mechanism mining coding. Background Technique

[0002] Blade design plays a crucial role in the design of turbomachinery. The analysis of its aerodynamic performance mainly relies on the computational fluid dynamics (CFD) method by calculating the physical field in the flow passage. However, a large number of computational grids make the calculation process time-consuming and laborious. At the same time, the highly non-linear characteristics of the flow field data also lead to low data analysis efficiency. In recent years, with the progress of deep learning technology, the academic community has begun to attempt to use the end-to-end data-driven method of neural networks to reduce the design cost and improve efficiency. For example, in the paper "C(NN)FD – A Deep Learning Framework for Turbomachinery CFD Analysis" published by Bruni et al. in 《IEEE Transactions on Industrial Informatics》 in 2024, taking the 1.5-stage compressor rotor blade as the research object, a C(NN)FD model was constructed to predict the influence of the tip clearance size of the rotor blade on the flow fields of multiple axial two-dimensional sections in the stage flow passage; in the paper "A fast prediction model of blade flutter in turbomachinery based on graph convolutional neural network" published by Liu et al. in 《Aerospace Science and Technology》 in the same year, a graph data structure was used to describe the node and element information of the CFD grid, and combined with a flow field prediction model and an aerodynamic damping prediction model based on a graph neural network to predict the flutter situation of a two-dimensional cascade under the action of the flow field. Nevertheless, the current data-driven aerodynamic performance prediction method completely relies on the modeling of flow field data, which limits its generalization ability.

[0003] In addition, the "black box" characteristic inherent in neural networks makes it difficult to gain trust in end-to-end data-driven methods for some key tasks. Since Raissi et al. proposed the Physics-informed Neural Networks (PINN) in their 2019 paper "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations" in the Journal of Computational Physics, by encoding the governing differential equations in the physical system into the loss function of the model, physical knowledge is introduced during the data fitting process, thus partially alleviating the problem of the opaque working mechanism of the model and becoming a current research hotspot. However, for the field of actual engineering simulation, taking the aerodynamic calculation of blades as an example, the popularization of such methods still faces multiple limitations such as complex computational domains, large data scales, and empirical formulas included in the mechanism knowledge. Summary of the Invention

[0004] The purpose of this application is to provide a method for predicting the meridional flow field of blades based on explicit and implicit mechanism mining and encoding, which can achieve fast and accurate prediction of the meridional flow field of the blade stage of an axial compressor.

[0005] To achieve the above purpose, this application provides the following solutions: A method for predicting the meridional flow field of blades based on explicit and implicit mechanism mining and encoding, comprising the following steps: Obtain the meridional grid of the blade passage on the axial compressor and the design condition parameters described by the graph data structure.

[0006] Using the trained meridional flow field prediction model of the blade, according to the meridional grid of the blade passage and the design condition parameters, predict the physical field data of each node of the meridional grid of the blade passage; the trained meridional flow field prediction model of the blade is a model obtained by training the meridional flow field prediction model of the blade using the model training strategy with explicit encoding of the through-flow mechanism; the model training strategy with explicit encoding of the through-flow mechanism is to explicitly encode the through-flow analysis mechanism of the turbine into the model loss function, and based on the model loss function during the training process, optimize the meridional flow field prediction model of the blade through backpropagation; the meridional flow field prediction model of the blade is a graph neural network model based on the implicit mechanism mining mechanism; the implicit mechanism mining mechanism is a mechanism for mining the implicit differential correlation relationship inside the physical data as data features during the data feature extraction process of the graph neural network model.

[0007] According to the specific embodiments provided by this application, the following technical effects are disclosed: The present application provides a method for predicting the meridional flow field of a blade based on explicit and implicit mechanism mining encoding. In this method, during the data feature extraction process of the graph neural network model, an implicit differential correlation relationship inside the physical data is mined through an implicit mechanism mining mechanism as data features, and the turbine flow analysis mechanism is explicitly encoded into the model loss function. The blade meridional flow field prediction model is trained using a strategy of optimizing the model through backpropagation based on the model loss function, so that the trained blade meridional flow field prediction model can predict the physical field data of each node of the meridional plane grid of the blade flow passage according to the meridional plane grid of the blade flow passage described by the graph data structure and the design condition parameters. By mining the implicit differential correlation inside the physical data during the data feature extraction process, the present application improves the accuracy of predicting the meridional flow field of the blade. Additionally, by explicitly encoding the turbine flow analysis mechanism into the model loss function to constrain the training process, the generalization ability of the model and the confidence level of the results are enhanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0009] Figure 1 It is a flowchart of a method for predicting the meridional flow field of a blade based on explicit and implicit mechanism mining encoding provided by an embodiment of the present application.

[0010] Figure 2 It is a flowchart of constructing and training a blade meridional flow field prediction model in a method for predicting the meridional flow field of a blade based on explicit and implicit mechanism mining encoding provided by an embodiment of the present application.

[0011] Figure 3 It is a flowchart of step B1 in a method for predicting the meridional flow field of a blade based on explicit and implicit mechanism mining encoding provided by another embodiment of the present application.

[0012] Figure 4 It is a schematic structural diagram of a blade meridional flow field prediction model in a method for predicting the meridional flow field of a blade based on explicit and implicit mechanism mining encoding provided by another embodiment of the present application.

[0013] Figure 5 It is a schematic structural diagram of a spatial-spectral regularization graph neural operator unit in a method for predicting the meridional flow field of a blade based on explicit and implicit mechanism mining encoding provided by another embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0014] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0015] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0016] A method for predicting the meridional flow field of a blade based on explicit and implicit mechanism mining coding provided by an embodiment of the present application. In an exemplary embodiment, as Figure 1 shown, it includes the following steps: A1. Obtain the meridional plane grid and design condition parameters of the blade flow passage on the axial compressor described by the graph data structure.

[0017] A2. Use the trained blade meridional flow field prediction model to predict the physical field data of each node of the meridional plane grid of the blade flow passage according to the meridional plane grid of the blade flow passage and the design condition parameters.

[0018] Specifically, the trained blade meridional flow field prediction model used in step A2 is a model obtained by training the blade meridional flow field prediction model using the model training strategy of explicit coding of the through-flow mechanism; the model training strategy of explicit coding of the through-flow mechanism is to explicitly code the turbine through-flow analysis mechanism into the model loss function, and based on the model loss function during the training process, optimize the blade meridional flow field prediction model through backpropagation; the blade meridional flow field prediction model is a graph neural network model based on the implicit mechanism mining mechanism; the implicit mechanism mining mechanism is a mechanism for mining the implicit differential correlation relationship inside the physical data as data features during the data feature extraction process of the graph neural network model.

[0019] In this embodiment, the design condition parameters of the blade flow passage include the rotor speed, inlet total pressure, inlet total temperature, and outlet static pressure; the physical field data of each node of the meridional plane grid includes pressure, density, temperature, and velocity.

[0020] Before using the trained blade meridional flow field prediction model in step A2, obviously, the method for predicting the meridional flow field of a blade based on explicit and implicit mechanism mining coding in this embodiment also requires a process of constructing and training the blade meridional flow field prediction model, as Figure 2 shown, this process includes the following steps: B1. Through computational fluid dynamics simulation, a flow field data sample set is constructed; any flow field data sample in the flow field data sample set includes the meridian plane grid of the blade passage described by the graph data structure, the design condition parameters, and the physical field data of each node of the meridian plane grid. In this embodiment, as Figure 3 shown, step B1 specifically includes the following steps: B11. Divide the computational grid for the geometric model of the blade passage on the axial flow compressor to obtain the meridian plane grid of the blade passage.

[0021] B12. Through the Latin hypercube random sampling method, perform several samplings on the design condition parameters of the blade passage to obtain several groups of design condition parameters.

[0022] B13. For any group of design condition parameters, perform fluid dynamics calculations according to the meridian plane grid and the design condition parameters to obtain the physical field data on each node grid of the meridian plane grid.

[0023] B14. Calculate the geometric model of the blade passage through the circumferential averaging method to obtain the physical field data of each node of the meridian plane grid.

[0024] Specifically, first divide the computational grid for the geometric model of the axial flow compressor blades and passages, sample the four design condition parameters of rotor speed, inlet total pressure, inlet total temperature, and outlet static pressure through the Latin hypercube random sampling method to obtain 1000 calculation model samples under different design condition parameters; calculate all the calculation model samples through the CFD method to obtain the calculation results of pressure, density, temperature, and velocity on each node grid in the passage; calculate the geometric model of the blade passage through the circumferential averaging method to obtain the meridian plane data grid that is uniform in the axial and radial directions and used to characterize the meridian plane flow field and the physical field data of each node on it.

[0025] B15. Convert the meridian plane grid of the blade passage, the design condition parameters, and the physical field data of each node of the meridian plane grid into the form described by the graph data structure and use it as a flow field data sample; the flow field data sample includes sample features and sample labels; the sample features are the meridian plane grid and the design condition parameters described by the graph data structure; the sample labels are the meridian plane grid and the physical field data of each node of the meridian plane grid described by the graph data structure.

[0026] Express the meridian plane grid and the physical field data of each node of the meridian plane grid through the mathematical definition of the graph G ={ V , E}, where V is the node set of the meridian plane grid, ERepresents the connection relationship between each node, and it is considered that there is an edge connection relationship between the nodes that belong to the same meridian plane grid cell; the graph data can be represented by a feature matrix and a symmetric adjacency matrix as follows: .

[0027] Among them, n is the number of nodes, d is the node feature dimension, represents the i th node feature of the j th grid node; represents that there is an edge connection between node and , represents that there is no edge connection between node and ; The spatial coordinates of each node and the four design condition parameters under this sample are used as input features together; the output features are the density, pressure, temperature and velocity values at this node, that is, the physical field data. The meridian plane grid coordinates of each sample i and the four design variables of the rotor speed, inlet total pressure, inlet total temperature and outlet static pressure corresponding to the sample are used as graph node features together, and the adjacency relationship between the meridian plane grid nodes is used as graph edge connection information to obtain the input parameter graph ; The calculation results of the pressure, density, temperature and velocity of the meridian plane grid nodes of each sample i are used as graph node features, and the adjacency relationship between the meridian plane grid nodes is used as graph edge connection information to obtain the physical field graph ; Among them, the subscript i represents each sample, and 1 and 2 represent the design condition parameters and physical field parameters respectively.

[0028] Taking the input parameter graph i extracted by calculation for each sample as the sample feature, and the meridian plane physical field graph as the sample label, they are used together as a flow field data sample described by the graph data structure to obtain a sample set of blade calculation grid information, design condition parameters and meridian plane physical field data. The scale of the sample set is 1000 flow field data samples, and the 1000 flow field data samples are divided into a training set, a validation set and a test set in the ratio of 8:1:1 in turn, taking into account ensuring model training verification and generalization testing.

[0029] B2. Build a graph neural network model based on the implicit mechanism mining mechanism to obtain a blade meridional flow field prediction model; as Figure 4 shown, the blade meridional flow field prediction model includes a first fully connected layer, a graph information extraction network module and a regressor module.

[0030] Specifically, the first fully connected layer is used to transform the node features from the input dimension to the model calculation dimension through a fully connected transformation; preferably, the model calculation dimension is selected as 64.

[0031] The graph information extraction network module has an encoder-decoder structure, including an encoder path and a decoder path; the encoder path includes several sequentially connected encoder blocks, and the several encoder blocks are used to sequentially extract high-level feature information from the input data; the decoder path includes several sequentially connected decoder blocks, and the several decoder blocks are used to restore the feature maps of different sizes for the input features; the encoder blocks and decoder blocks of the same scale fuse different-level information through residual connections; the last decoder block outputs a high-level feature map with multi-level and multi-scale feature information fusion; the regressor module is used to perform regression calculations based on the high-level feature map to obtain the physical field data of each node of the meridian plane grid.

[0032] The graph encoding after dimension elevation is input into the encoder path of the graph information extraction network module based on the encoder-decoder structure, and high-level feature information is sequentially extracted through 3 sequentially connected encoder blocks; the resulting feature map output by the encoder path is input into the decoder path, and the feature map size is restored through 3 sequentially connected decoder blocks; in addition, the results of the decoder blocks and encoder blocks of the same size fuse different-level information through residual connections; finally, a high-level feature map with multi-level and multi-scale fusion is obtained; the high-level feature map is input into the regressor module to complete the regression calculation from the high-level features to the physical field parameters of the meridian plane nodes.

[0033] The encoder block includes a spatio-spectral regularized graph neural operator unit, a GELU activation function, and a graph pooling layer; preferably, the graph pooling layer is a gPooling layer, and the node selection rate of each layer is set to 0.8; the decoder block includes a graph upsampling layer, a GELU activation function, and a spatio-spectral regularized graph neural operator unit; preferably, the graph upsampling layer is a gUnPooling layer; as Figure 5 shown, the spatio-spectral regularized graph neural operator unit includes a spectral branch, a spatial branch, a splicing mapping layer, a residual direct connection branch, and a GELU function layer; after the output results of the spectral branch and the spatial branch are vectorially spliced, they are mapped back to the input dimension through the splicing mapping layer, and then superimposed with the results of the residual direct connection branch, and nonlinearly activated through the GELU function to obtain the output of the spatio-spectral regularized graph neural operator unit; the spatio-spectral regularized graph neural operator unit serves as the basic graph information aggregation layer of the blade meridional flow field prediction model, and mines the implicit differential correlation relationship inside the physical data as data features during the data feature extraction process.

[0034] The spectral branch includes a kernel integration block and a first hybrid regularization block; the kernel integration block includes a non-linear path, a linear path, and a first adder; the non-linear path contains a graph Fourier transform layer, a kernel integration layer, and a graph inverse Fourier transform layer connected in sequence; the linear path contains a linear transformation layer; the transformation process of the non-linear path can be summarized as the following formula: .

[0035] Wherein, y represents the output result of the non-linear path, D represents the degree matrix of the input graph, I is the identity matrix, is the regularized graph Laplacian matrix, Q is the eigenvector matrix of the graph Laplacian matrix, is the eigenvalue matrix of the graph Laplacian matrix. The graph Fourier transform of the eigenmatrix is achieved through . K is the graph integration kernel, is the diagonal filter learned from the data, which directly parameterizes the kernel in the spectral domain, represents element-wise multiplication; the matrix A is the adjacency matrix of the graph, represents whether there is a connection relationship between nodes i and j in the graph. If there is a connection, it is 1; if not, it is 0.

[0036] The output ends of the non-linear path and the linear path are respectively connected to an input end of the first adder, and the output end of the first adder is connected to the first hybrid regularization block; the first hybrid regularization block includes a global regularization path, a local regularization path, and a second adder; the output ends of the global regularization path and the local regularization path are respectively connected to an input end of the second adder; the output of the second adder is comprehensively regularized through trainable scaling coefficients and translation coefficients; wherein, preferably, the global regularization path includes a GraphNorm layer, and the local regularization path includes a LayerNorm layer; the calculation process of the hybrid regularization block can be summarized as: .

[0037] Wherein, h is the encoded graph node information matrix, and respectively represent the output results of the LayerNorm layer and the GraphNorm layer; and represent trainable gating parameters, having the same shape as , Same matrix dimensions; and represent trainable scaling and translation parameter matrices, and are the trainable scaling parameter matrix and translation parameter matrix in the LayerNorm layer, and are the trainable scaling parameter matrix and translation parameter matrix in the GraphNorm layer, dynamically transforming the two regularization results to obtain the final hybrid regularization result; and are the feature mean vector and standard deviation vector calculated for each graph node according to the feature dimension in the LayerNorm layer, represents the i th j value of the node in the th feature dimension, j and n are the feature mean and feature standard deviation of the th dimension in the calculation batch respectively; and are the mean vector and standard deviation vector calculated according to the graph dimension in the GraphNorm layer, j and n are the feature mean and feature standard deviation of the th dimension in the calculation batch respectively; j is the number of samples in the batch;

[0038] The spatial branch includes a graph convolutional layer and a second hybrid regularization block; the output end of the graph convolutional layer is connected to the input end of the second hybrid regularization block; the structure of the second hybrid regularization block is exactly the same as that of the first hybrid regularization block. Preferably, the graph convolutional layer in the spatial branch is a SAGEConv layer.

[0039] The regressor module includes a second fully connected layer, a RELU function layer, and a third fully connected layer; the second fully connected layer halves the feature dimension of the input reconstructed graph encoded, and after non-linear activation through the RELU function layer, the output result is regressed through the third fully connected layer. In one embodiment, the output result with a feature dimension of 6 is regressed through the third fully connected layer, that is, the pressure, temperature, density, and velocity components in three coordinate directions of each node in the meridional plane flow field.

[0040] B3. Based on the flow field data sample set, adopt a model training strategy with explicit coding of the through-flow mechanism to train the blade meridional flow field prediction model, and obtain a trained blade meridional flow field prediction model.

[0041] Jointly input the physical field data predicted by the model and the physical field data corresponding to the sample labels into the model loss function with explicit coding of the mechanism, and update the network parameters of the blade meridional flow field prediction model through the loss function value until the model converges.

[0042] Specifically, the model loss function of the blade meridional flow field prediction model includes a numerical deviation loss term, a control equation residual loss term, and a boundary condition residual loss term; optimize and update the parameters of each layer of the blade meridional flow field prediction model through the backpropagation process until the model converges. The numerical deviation loss term is the loss value obtained by normalizing the absolute error between the physical field data predicted by the model and the physical field data corresponding to the sample labels; the control equation residual loss term is based on the meridional velocity gradient equation in the through-flow analysis of the turbine as the control equation, calculate the residuals respectively according to the physical field data predicted by the model and the physical field data corresponding to the sample labels, and determine the loss value according to the deviation of the residual values of the two; the boundary condition residual loss term is the satisfaction of the physical field data predicted by the model with the boundary conditions given by the input samples. In this embodiment, the model loss function of the blade meridional flow field prediction model is shown as the following formula: .

[0043] Among them, TotalLoss is the model loss value of the blade meridional flow field prediction model, l reg is the value of the numerical deviation loss term, l res is the value of the control equation residual loss term, l bc is the value of the boundary condition residual loss term, w 1, w 2, and w 3 are the weights of the numerical deviation loss term, the control equation residual loss term, and the boundary condition residual loss term respectively.

[0044] The numerical deviation loss term can be calculated according to the following formula; .

[0045] Among them, d is the total number of physical field parameter values, l is the label of the physical field parameter value, n is the total number of nodes of the meridional plane grid, i is the node label, and respectively represent the physical field data output by the model prediction and the physical field parameter value at the i th node in the physical field data corresponding to the sample label. | | is the absolute value symbol. l th physical field parameter value. and respectively represent the maximum and minimum values of the l th physical field parameter value in the corresponding physical field data.

[0046] The residual loss term of the governing equation can be calculated according to the following formula: .

[0047] Among them, is the residual value obtained by substituting the physical field parameter value at the i th node in the physical field data output by the model prediction into the governing equation of the turbine through-flow analysis mechanism. is the residual value obtained by substituting the physical field parameter value at the i th node in the physical field data corresponding to the sample label into the governing equation of the turbine through-flow analysis mechanism. A , B , C are the coefficients of the governing equation of the turbine through-flow analysis mechanism. w i is the relative velocity of the gas in the flow field relative to the rotor blade at the i th node. q is the streamline where the i th node is located.

[0048] The governing equation of the turbine through-flow analysis mechanism is shown as follows: .

[0049] Among them, w is the relative velocity of the gas in the flow field relative to the rotor blade. represents the derivative of the gas velocity with respect to the direction of the quasi-orthogonal line of the streamline where it is located. , , represent the derivatives of the respective coordinates in the cylindrical coordinate system with respect to the direction of the quasi-orthogonal line of the streamline where they are located. represents the flow direction angle, which is the angle between the relative velocity and the meridian streamline where the point is located. represents the flow inclination angle, which is the angle between the meridional relative velocity w m and the axial direction. The meridional relative velocity is defined as the projection velocity of the gas relative velocity on the meridional plane. is the meridional relative velocity w m with respect to the direction of the meridian streamline. is the curvature of the streamline where each point is located.r is the radial coordinate in the rotor coordinate system; is the angular velocity of rotor rotation; represents the derivatives of the total enthalpy, angular momentum, and entropy at the inlet section with respect to the direction of the quasi-orthogonal line of the streamline where they are located, T is the temperature.

[0050] The boundary condition residual loss term is the satisfaction of the physical field data predicted by the model with the boundary conditions given by the input samples. Specifically, it includes calculating the absolute deviation mean of the predicted total pressure and total temperature at the meridional plane inlet boundary, and the static pressure at the outlet boundary with the given total pressure at the inlet, total temperature at the inlet, and static pressure at the outlet boundary conditions, and the sum of these three is used as the boundary condition residual loss term; During the training process of the blade meridional flow field prediction model, whenever a batch of training data undergoes the forward process, calculate the numerical deviation loss based on the results of the forward prediction output and the physical field data corresponding to the labels l reg , the control equation residual loss l res and the boundary condition residual loss l bc and use the training loss to update the network weights during the backpropagation process until the training of the blade meridional flow field prediction model converges.

[0051] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0052] In this article, specific examples are used to elaborate on the principles and implementation methods of this application. The descriptions of the above embodiments are only used to help understand the method and its core idea of this application; at the same time, for those of ordinary skill in the art, according to the idea of this application, there will be changes in the specific implementation methods and application scopes. In summary, the content of this specification should not be construed as a limitation to this application.

Claims

1. A method for predicting the meridional flow field of a blade based on explicit and implicit mechanism mining coding, characterized in that, Including: Obtain the meridional plane grid and design condition parameters of the blade flow passage on the axial compressor described by the graph data structure; Using the trained blade meridional flow field prediction model, according to the meridional plane grid and design condition parameters of the blade flow passage, predict the physical field data of each node of the meridional plane grid of the blade flow passage; The trained blade meridional flow field prediction model is a model obtained by training the blade meridional flow field prediction model using the model training strategy of explicit encoding of the flow-through mechanism; the model training strategy of explicit encoding of the flow-through mechanism is to explicitly encode the turbine flow-through analysis mechanism into the model loss function, and based on the model loss function during the training process, optimize the blade meridional flow field prediction model through backpropagation; the blade meridional flow field prediction model is a graph neural network model based on the implicit mechanism mining mechanism; the implicit mechanism mining mechanism is a mechanism for mining the implicit differential correlation relationship inside the physical data as data features during the data feature extraction process of the graph neural network model.

2. The blade meridional flow field prediction method based on explicit and implicit mechanism mining coding according to claim 1, wherein Before using the trained blade meridional flow field prediction model to predict the physical field data of each node on the meridional plane of the blade flow passage according to the meridional plane grid and design condition parameters of the blade flow passage, the blade meridional flow field prediction method based on explicit and implicit mechanism mining and encoding further includes: Construct a flow field data sample set through computational fluid dynamics simulation; any flow field data sample in the flow field data sample set includes the meridional plane grid of the blade flow passage described by the graph data structure, design condition parameters, and physical field data of each node of the meridional plane grid; Construct a graph neural network model based on the implicit mechanism mining mechanism to obtain a blade meridional flow field prediction model; the blade meridional flow field prediction model includes a first fully connected layer, a graph information extraction network module, and a regressor module; According to the flow field data sample set, use the model training strategy of explicit encoding of the flow-through mechanism to train the blade meridional flow field prediction model to obtain a trained blade meridional flow field prediction model.

3. The blade meridional flow field prediction method based on explicit and implicit mechanism mining coding according to claim 2, characterized in that, Constructing a flow field data sample set through computational fluid dynamics simulation specifically includes: Divide the computational grid of the geometric model of the blade flow passage on the axial compressor to obtain the meridional plane grid of the blade flow passage; Perform several samplings on the design condition parameters of the blade flow passage by the Latin hypercube random sampling method to obtain several groups of design condition parameters; For any group of design condition parameters, perform fluid dynamics calculations according to the meridional plane grid and design condition parameters to obtain the physical field data on each node grid of the meridional plane grid; Calculate the geometric model of the blade flow passage by the circumferential averaging method to obtain the physical field data of each node of the meridional plane grid; Convert the meridian plane grid of the blade passage, the design condition parameters, and the physical field data of each node of the meridian plane grid into a form described by a graph data structure, and use it as a flow field data sample; the flow field data sample includes sample features and sample labels; the sample features are the meridian plane grid and design condition parameters described by the graph data structure; the sample labels are the meridian plane grid and the physical field data of each node of the meridian plane grid described by the graph data structure.

4. The method for predicting the meridional flow field of a blade encoded based on the explicit and implicit mechanism mining according to any one of claims 1-3, characterized in that, The design condition parameters of the blade passage include rotor speed, inlet total pressure, inlet total temperature, and outlet static pressure; the physical field data of each node of the meridian plane grid includes pressure, density, temperature, and velocity.

5. The blade meridional flow field prediction method based on explicit and implicit mechanism mining coding according to claim 2, wherein The first fully connected layer is used to transform the features of each node from the input dimension to the model calculation dimension through a fully connected transformation; the graph information extraction network module is based on an encoder-decoder structure, including an encoder path and a decoder path; the encoder path includes a number of sequentially connected encoder blocks, and a number of the encoder blocks are used to sequentially extract high-level feature information from the input data; the decoder path includes a number of sequentially connected decoder blocks, and a number of the decoder blocks are used to recover feature maps of different sizes for the input features. Different levels of information are fused through residual connections between encoder blocks and decoder blocks of the same scale; the last decoder block outputs a high-level feature map with multi-level and multi-scale feature information fusion; the regressor module is used to perform regression calculations based on the high-level feature map to obtain the physical field data of each node of the meridian plane grid.

6. The method for predicting the meridional flow field of a blade based on explicit and implicit mechanism mining coding according to claim 5, characterized in that The encoder block includes a spatio-spectral regularization graph neural operator unit, a GELU activation function, and a graph pooling layer; the decoder block includes a graph upsampling layer, a GELU activation function, and a spatio-spectral regularization graph neural operator unit; the spatio-spectral regularization graph neural operator unit includes a spectral branch, a spatial branch, a concatenation mapping layer, a residual direct connection branch, and a GELU function layer; after the output results of the spectral branch and the spatial branch are vectorially concatenated, they are mapped back to the input dimension through the concatenation mapping layer, and then superimposed with the results of the residual direct connection branch, and non-linearly activated through the GELU function to obtain the output of the spatio-spectral regularization graph neural operator unit; the spatio-spectral regularization graph neural operator unit serves as the basic graph information aggregation layer of the blade meridional flow field prediction model, and mines the implicit differential correlation relationship inside the physical data as data features during the data feature extraction process.

7. The prediction method of the blade meridional flow field based on explicit and implicit mechanism mining coding according to claim 6, characterized in that The spectral branch includes a kernel integration block and a first hybrid regularization block; the kernel integration block includes a non-linear path, a linear path, and a first adder; the non-linear path includes a graph Fourier transform layer, a kernel integration layer, and a graph inverse Fourier transform layer connected in sequence; the linear path includes a linear transformation layer; the output ends of the non-linear path and the linear path are respectively connected to an input end of the first adder, and the output end of the first adder is connected to the first hybrid regularization block. The first hybrid regularization block includes a global regularization path, a local regularization path, and a second adder; the output ends of the global regularization path and the local regularization path are respectively connected to one input end of the second adder; the output of the second adder is comprehensively regularized through trainable scaling coefficients and translation coefficients; the spatial branch includes a graph convolutional layer and a second hybrid regularization block; the output end of the graph convolutional layer is connected to the input end of the second hybrid regularization block; The structure of the second hybrid regularization block is exactly the same as that of the first hybrid regularization block.

8. The method for predicting the meridional flow field of a blade encoded based on the explicit and implicit mechanism mining according to claim 2, wherein The regressor module includes a second fully connected layer, a RELU function layer, and a third fully connected layer; the second fully connected layer halves the feature dimension encoded by the input reconstructed graph, and after non-linearly activating through the RELU function layer, the output result is regressed through the third fully connected layer.

9. The method for predicting the meridional flow field of a blade encoded based on the explicit and implicit mechanism mining according to claim 1, wherein The model loss function of the blade meridional flow field prediction model includes a numerical deviation loss term, a control equation residual loss term, and a boundary condition residual loss term; the numerical deviation loss term is a loss value obtained by normalizing the absolute error between the physical field data predicted by the model and the physical field data corresponding to the sample label; the control equation residual loss term is a loss value determined by taking the meridional velocity gradient equation in the turbomachinery through-flow analysis as the control equation, calculating the residuals respectively according to the physical field data predicted by the model and the physical field data corresponding to the sample label, and based on the deviation of the residual values of the two; the boundary condition residual loss term is the satisfaction degree of the physical field data predicted by the model with respect to the boundary conditions given by the input samples.

10. The method for predicting the meridional flow field of a blade encoded based on the explicit and implicit mechanism mining according to claim 1, wherein The model loss function of the blade meridional flow field prediction model is shown as the following formula: ； Among them, TotalLoss is the model loss value of the meridional flow field prediction model of the blade, l reg is the value of the numerical deviation loss term, l res is the value of the control equation residual loss term, l bc is the value of the boundary condition residual loss term, w 1, w 2, and w 3 are the weights of the numerical deviation loss term, the control equation residual loss term, and the boundary condition residual loss term, respectively.

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