Virtual and real data fused space-time diagram neural network propeller flow field prediction method

Abstract

The invention discloses a virtual and real data fused space-time diagram neural network propeller flow field prediction method, and relates to the cross field of computational fluid mechanics and deep learning disciplinary. Establishing a local enhanced sub-graph structure between a flow field scatter feature set and main graph structure data based on a K-nearest neighbor strategy to obtain virtual and real data fused unified graph structure data, and training a network structure formed by an E (n) isovariant graph neural network model and a Transform model by using the unified graph structure data; unified graph structure data considers global coverage of numerical simulation data and local enhancement of physical test measurement data, the credibility of training samples is improved, and the advantages of spatial topology and time sequence evolution characteristics of a complex wake flow field of a ship propeller can be effectively captured in combination with a network structure. And the prediction precision of the complex wake flow field of the ship propeller is improved.

Description

Technical Field

[0001] This application relates to the interdisciplinary field of computational fluid dynamics and deep learning, and particularly to a method for predicting the propeller flow field using a spatio-temporal graph neural network with virtual-real data fusion. Background Art

[0002] During the navigation of a ship, the high-speed rotating propeller will form complex vortex structures and unsteady flow fields at the stern of the ship. Accurately predicting the wake flow field of the propeller is crucial for optimizing its propulsion efficiency and controlling vibration and noise. Traditional techniques mainly rely on numerical simulation and physical experiments. However, numerical simulation requires high-precision grid simulation in the propeller area and there are deviations, and physical experiments usually can only measure sparse scattered point data at local points.

[0003] To make up for the respective deficiencies of numerical simulation and physical experiments, with the rapid development of deep learning technology in solving engineering fluid mechanics problems, there are currently many studies using traditional random forest algorithms, multi-layer perceptrons, convolutional neural networks, and physics-informed neural networks and other methods to carry out research on the reconstruction or prediction of the flow field around ship propellers. However, these studies generally cannot capture the spatial topological features and distribution laws of complex flow fields, so the prediction accuracy is not ideal. Summary of the Invention

[0004] In view of the above problems and technical requirements, this application proposes a method for predicting the propeller flow field using a spatio-temporal graph neural network with virtual-real data fusion. The technical solution of this application is as follows: A method for predicting the propeller flow field using a spatio-temporal graph neural network with virtual-real data fusion, the spatio-temporal graph neural network propeller flow field prediction method includes: constructing a grid node feature set at any moment using the numerical simulation data of the ship propeller wake flow field and constructing a flow field scattered point feature set at any moment using the physical experiment measurement data of the ship propeller wake flow field ; wherein, the grid node feature set at each moment includes the spatial structure features between grid nodes and the simulated velocity at the current moment of the spatial coordinates of each grid node, and the flow field scattered point feature set at each moment includes the spatial coordinates of each flow field scattered point and the measured velocity at the current moment of each flow field scattered point; Using each grid node feature set to construct the main graph structure data, and establishing a local enhanced subgraph structure between the flow field scattered point feature set at the current moment and the main graph structure data based on the K-nearest neighbor strategy, to obtain the unified graph structure data with virtual-real data fusion at the current moment. There is a corresponding velocity value at each graph node in the unified graph structure data; Taking any TAt and before the moment M - The sequence formed by the unified graph structure data of the -1 most recent moments in chronological order is used as the sample input, and T the unified graph structure data at the +1 moment is used as the sample output to construct T the training samples corresponding to the moments, and the training samples corresponding to different moments are formed into a training sample set. The integer parameter M ≥2; For any T training sample corresponding to the moment, use the E(n)-equivariant graph neural network model to capture the spatial structure features of the unified graph structure data at each moment in the training sample respectively and output the updated node positions and velocity features of each graph node to form the velocity field feature at the current moment; input the feature time series sequence formed by the velocity field features at each moment in the training sample into the multi-head self-attention mechanism of the Transformer model to obtain T the predicted value of the velocity field feature at the +1 moment as the prediction result of the training sample; Combine the sample output and prediction result of each training sample, and use the training sample set to train the E(n)-equivariant graph neural network model and the Transformer model, and use the trained E(n)-equivariant graph neural network model and Transformer model to predict the wake field of the ship propeller.

[0005] Its further technical solution is that using the E(n)-equivariant graph neural network model to output the velocity field feature at each moment includes: Initialize the first-layer graph convolution of the E(n)-equivariant graph neural network model according to the input unified graph structure data to obtain any graph node in the unified graph structure data j at the node position and velocity feature , where j is the node position of the graph node in the unified graph structure data, and j is the velocity value of the graph node in the unified graph structure data; l Introduce the propeller rotation prior function to perform message passing from the l -th layer of graph convolution to the 1 -th layer of graph convolution, and update according to the spatial structure features of the l -th layer of graph convolution to obtain the node position j of the graph node l at the 1 + -th layer of graph convolution and the velocity feature ; The velocity field feature at the current moment is obtained by integrating the node positions and velocity features of each graph node in the last layer of graph convolution.

[0006] Its further technical solution is to update the obtained graph node j at the l + 1 -th layer of graph convolution for the node position and velocity feature including: Determine any graph node l adjacent to the graph nodes based on the node positions of each node in the j -th layer of graph convolution, calculate the message vector j between the graph node i and any adjacent graph node , where is the velocity feature of the graph node i in the l -th layer of graph convolution, is the node distance between the graph node j and the graph node i in the l -th layer of graph convolution, is a learnable multi-layer perceptron; Based on the message vector j between the graph node i and all its adjacent graph nodes and combined with the propeller rotation prior function to update the obtained graph node j at the l + 1 -th layer of graph convolution for the node position and velocity feature ; where the propeller rotation prior function is determined according to the kinematic function and is related to the propeller rotation speed and the rotation angle of the propeller per unit time .

[0007] Its further technical solution is to update the obtained graph node j at the l + 1 -th layer of graph convolution for the node position and velocity feature as:

[0008] where is the node position of the graph node i in the l -th layer of graph convolution, , is thel Graph nodes in layer graph convolution j and all its adjacent graph nodes i The message vectors between constitute a set, and are respectively learnable multi-layer perceptrons.

[0009] Its further technical solution is that obtaining the unified graph structure data of current virtual-real data fusion includes: Regarding each grid node in the grid node feature set at the current moment as a graph node in the main graph structure data sim , the connections between grid nodes form bidirectional edges between the corresponding graph nodes in the main graph structure data sim to construct the main graph structure data at the current moment, and the spatial coordinates of each grid node are used as the node positions of the corresponding graph nodes in the main graph structure data sim , the simulated velocity at the grid node is used as the velocity value at the corresponding graph node sim ; For any flow field scatter point in the flow field scatter point feature set at the current moment , when the spatial coordinates of the flow field scatter point coincide with the node positions of the graph nodes formed by grid nodes in the main graph structure data sim , the measured velocity at the flow field scatter point is used to correct the velocity value at the coincident graph node sim to , where the fusion weight coefficient ; When the spatial coordinates of the flow field scatter point do not coincide with the node positions of all graph nodes in the main graph structure data, the flow field scatter point is used as a newly added graph node exp , the spatial coordinates of the flow field scatter point are used as the node positions of the corresponding newly added graph node exp , the measured velocity at the flow field scatter point is used as the velocity value at the corresponding newly added graph node exp , and the neighbor graph nodes of the newly added graph node in the main graph structure data are searched based on the K-nearest neighbor strategy, and bidirectional edges are respectively established between the newly added graph node exp and each of its neighbor graph nodes to form a local enhanced subgraph structure with the main graph structure data. exp

[0010] Its further technical solution is that obtaining the unified graph structure data of current virtual-real data fusion also includes: When a newly added graph node at any flow field scatter point​​​a The graph nodes with its neighbors b The bidirectional edges established With the bidirectional edges already existing in the main graph structure data When crossing, at the bidirectional edges And the bidirectional edges Add a new graph node at the crossing position of intp , and according to the graph node a , graph node b , graph node c And graph node d Interpolate the node positions and velocity values of each to obtain the node position and velocity value of graph node intp ; Among them, graph node c And graph node d Are the graph nodes at both ends of the bidirectional edge .

[0011] Its further technical solution is that interpolating to obtain the node position and velocity value of graph node intp Includes: According to the node position of graph node a And the node position of the neighbor graph node b Calculate the parametric equation of the bidirectional edge , according to the node position of graph node c And the node position of graph node d Calculate the parametric equation of the bidirectional edge , use the parametric equation of the bidirectional edge And the parametric equation of the bidirectional edge Calculate the intersection position as the node position of graph node intp ; Interpolate to determine the velocity value at graph node intp Is:

[0012] Among them, Is the velocity value at graph node a , Is the velocity value at graph node b , Is the velocity value at graph node c , Is the velocity value at graph node d .

[0013] Its further technical solution is that the unified graph structure data includes Graph nodes formed by grid nodes sim , Graph nodes formed by flow field scatter points​​exp , and a newly added graph node at the bidirectional edge crossing position intp ; The spatio-temporal graph neural network propeller flow field prediction method further includes: Using the neural network automatic differentiation mechanism according to the total loss function to perform model training, the total loss function ; where is the numerical simulation data loss term calculated using the graph nodes formed by the grid nodes in the unified graph structure data sim , is the experimental scatter point supervision term calculated using the graph nodes formed by the flow field scatter points in the unified graph structure data exp , is the interpolation node data error term calculated using the newly added graph nodes at the bidirectional edge crossing position in the unified graph structure data intp , is the N-S physical equation regularization term calculated using all graph nodes in the unified graph structure data combined with the N-S physical equation; , , are weight coefficients respectively.

[0014] Its further technical solution is that the calculation formulas for each item in the total loss function are:

[0015]

[0016]

[0017]

[0018] where is the predicted velocity value at the graph node j in the prediction result of the training sample, is the actual velocity value at the graph node j in the sample output of the training sample; is the set composed of all graph nodes formed by grid nodes in the unified graph structure data sim , is the set composed of all graph nodes formed by flow field scatter points in the unified graph structure data exp , is the set composed of all newly added graph nodes at the bidirectional edge crossing position in the unified graph structure data intp ; is the number of collocation points of the N-S physical equation, is the graph node The predicted velocity value at is calculated by using the velocity predicted value at the graph node and combining with the N - S physical equation to obtain the pressure value at the graph node , where is the Reynolds number, and is the Laplace operator.

[0019] Its further technical solution is to use the trained E(n) - equivariant graph neural network model combined with the Transformer model to predict the wake flow field of the ship propeller, including: Obtain the flow field data of the ship propeller wake flow field at the initial consecutive ~M first time moments, and construct the actual graph structure data at the current moment according to the flow field data at each moment; Starting from t = M , use the E(n) - equivariant graph neural network model to extract the corresponding velocity field features respectively according to the actual graph structure data at the t moment and the previous M -1 nearest moments, and input the feature time - series sequence composed of the velocity field features extracted at the t moment and the previous M -1 nearest moments in chronological order into the multi - head self - attention mechanism of the Transformer model to obtain the predicted value of the velocity field feature at the t +1 moment and perform autoregressive forecasting.

[0020] The beneficial technical effect of this application is: This application discloses a spatio - temporal graph neural network propeller flow field prediction method for virtual - real data fusion. This method uses the network structure of the combined E(n) - equivariant graph neural network model and the Transformer model. When training the network structure, the physical test scatter data is incorporated into the numerical simulation data through the K - nearest neighbor strategy to construct a unified graph structure data for virtual - real fusion. Then, the unified graph structure data is used for model training. The unified graph structure data takes into account the global coverage of the simulation data and the local enhancement of the physical test scatter points, and also avoids the problem of low credibility when using only numerical simulation data to construct the training samples of the graph data structure. Combined with the characteristics that the network structure can effectively capture the spatial topology and temporal evolution characteristics of the complex wake flow field of the ship propeller, it can improve the prediction accuracy of the complex wake flow field of the ship propeller.

[0021] When using an E(n)-equivariant graph neural network model to capture spatial topological features, a propeller rotation prior function is introduced in the message passing calculation process, which can dynamically update the node positions in the propeller rotation area, making the simulated physical process closer to the actual situation and further improving the accuracy and precision of the flow field prediction.

[0022] Combining the numerical simulation data loss term, the experimental scatter supervision term, the interpolation node data error term, and the N-S physical equation regularization term to form a polynomial total loss function, and introducing adjustable hyperparameter weights, enabling the model to achieve an optimal balance between multi-source data and physical laws. Brief Description of the Drawings

[0023] Figure 1 It is a schematic flowchart of the spatio-temporal graph neural network propeller flow field prediction method in an embodiment of the present application.

[0024] Figure 2 It is a schematic diagram of obtaining unified graph structure data of virtual-real data fusion in a local area of the wake flow field in an example.

[0025] Figure 3 It is a schematic diagram of layer-by-layer message passing between graph convolutions in the E(n)-equivariant graph neural network model in an embodiment of the present application. Detailed Embodiment

[0026] The following further describes the detailed embodiment of the present application with reference to the drawings.

[0027] The present application discloses a spatio-temporal graph neural network propeller flow field prediction method for virtual-real data fusion. Please refer to Figure 1 the flowchart. The spatio-temporal graph neural network propeller flow field prediction method includes the following contents: Step S1, constructing a grid node feature set at any moment using the numerical simulation data of the ship propeller wake flow field and constructing a flow field scatter feature set at any moment using the physical test measurement data of the ship propeller wake flow field. .

[0028] The physical test measurement data are the measured values of physical quantities at different spatial coordinates in the ship propeller wake flow field obtained by using the particle tracking velocimetry method in the test water tank. The physical quantities that can be measured by the physical test are mainly velocity values. Therefore, in the present application, the obtained physical test measurement data include the velocity values measured at different spatial coordinates, and the present application refers to the measured velocity values as the measured velocities. The correspondingly constructed flow field scatter feature set at each moment includes the spatial coordinates of each flow field scatter and the measured velocity of the flow field scatter at the current moment, denoted as , where Indicates the spatial coordinates of the th flow field scatter point, and indicates the measured velocity at the th flow field scatter point, where is the total number of flow field scatter points included in the physical experiment measurement data. Due to the limitations of physical experiments, the total number of flow field scatter points in the flow field scatter point feature set

[0029] is relatively limited, and the spatial coordinates of different flow field scatter points are mainly distributed in the local area of the ship propeller wake flow field. The numerical simulation data is the data output by numerically simulating the ship propeller wake flow field using various existing computational fluid dynamics (CFD) software. For example, in one instance, the Star CCM+ computational fluid dynamics software is used to simulate the propeller wake flow field of the DTMB5415 open standard ship model to output numerical simulation data. Regardless of the specific data simulation method used, when performing numerical simulation, the computational domain of the ship propeller wake flow field is discretized into grids and then numerically simulated. The final output numerical simulation data includes grid data and physical quantity data. The grid data records the grid cell division method, and the physical quantity data records the physical quantity simulation results at each grid cell. Since the physical quantity obtained from the numerical simulation in this application needs to be merged with the physical experiment measurement results later, and as mentioned above, the physical quantity measured in the physical experiment is mainly the velocity value, the physical quantity data included in the numerical simulation data is also the simulation result of the velocity, which is called the simulated velocity in this application. The corresponding grid node feature set constructed for each moment includes the spatial structure features between grid nodes and the simulated velocity at the spatial coordinates of each grid node at the current moment, denoted as where represents the spatial coordinates of the th grid node, represents the simulated velocity at the th grid node, represents the edge index of the connection line between the th grid node and the th grid node, and represents the distance of the connection line between the th grid node and the th grid node, and where and where is the total number of grid nodes included in the numerical simulation data, is an integer parameter. According to the characteristics of numerical simulation data, the set of grid node features the total number of grid nodes in is relatively large, and the spatial coordinates of different grid nodes are distributed within the global range of the wake field of the ship propeller. It should be noted that the simulation results of physical quantities directly obtained from numerical simulation data are often the simulated velocities at the centers of grid cells. Then, methods such as mean calculation can be used to calculate the simulated velocities at each grid node, which will not be elaborated here.

[0030] Step S2: Use the set of grid node features at each moment to construct the main graph structure data, and establish the local enhanced subgraph structure between the set of flow field scatter point features at the current moment and the main graph structure data to obtain the unified graph structure data of virtual-real data fusion at the current moment. The constructed unified graph structure data includes a total of graph nodes. Any graph node j has a unique node position and the graph node j has a corresponding velocity value . The graph nodes are connected by bidirectional edges to form a specific spatial structure feature.

[0031] In one embodiment, constructing the unified graph structure data includes the following stages: (1) Construct the main graph structure data Take each grid node in the set of grid node features at the current moment as a graph node in the main graph structure data sim . The connections between the grid nodes form the bidirectional edges between the corresponding graph nodes sim in the main graph structure data to construct the main graph structure data at the current moment. In this application, this type of graph node is called the graph node formed by grid nodes sim .

[0032] For the graph node formed by any th grid node in the set of grid node features in the main graph structure data sim , the node position sim of this graph node is the spatial coordinate of the th grid node . The velocity value sim at this graph node is the simulated velocity at the th grid node . The bidirectional edge connection relationship between this graph node sim and other graph nodes is the same as that of the The connection relationship between a grid node and other grid nodes is consistent. Then, the graph nodes formed by the grid nodes in the main graph structure data sim The total number of is equal to the total number of grid nodes in the grid node feature set and is

[0033] In practical applications, by using a Python custom program to call the third-party function library of Pytorch Geometry, the main graph structure data can be constructed according to the grid node feature set .

[0034] (2) Establish the local enhanced sub-graph structure between the flow field scatter point feature set and the main graph structure data.

[0035] Process each flow field scatter point in the flow field scatter point feature set at the current moment one by one. For any th flow field scatter point, it is processed in the following two cases: (a) When the spatial coordinates of the th flow field scatter point coincide with the node position of the graph node sim formed by the grid nodes in the main graph structure data, the measured velocity at the flow field scatter point is used to correct the velocity value at the coincident graph node sim . Among them, when the spatial coordinates of the th flow field scatter point and the node position of any graph node sim have an Euclidean distance less than the distance threshold, it is determined that they coincide; otherwise, it is determined that they do not coincide. When they coincide, the th flow field scatter point is not added to the main graph structure data and is only used to correct the velocity value at the graph node sim coincident with it. After correcting the velocity value, the graph node still belongs to the graph node sim formed by the grid nodes.

[0036] In one embodiment, the measured velocity at the th flow field scatter point is used to correct the velocity value sim at the coincident graph node , where is the velocity value at the graph node formed by the grid nodes in the main graph structure data and coincident with the sim th flow field scatter point, is the corrected velocity value at the graph node coincident with the sim th flow field scatter point, and the fusion weight coefficient . In an application example, the fusion weight coefficient .

[0037] (b) When the spatial coordinates of the th flow field scatter point do not coincide with the node positions of all the graph nodes in the main graph structure data, the th flow field scatter point is taken as a newly added graph node exp , and the spatial coordinates of the th flow field scatter point are used as the node position exp of the corresponding newly added graph node 、the measured velocity at the th flow field scatter point is used as the velocity value exp at the corresponding newly added graph node .

[0038] Then, based on the K-nearest neighbor strategy, search for the neighbor graph nodes of the newly added graph node exp in the main graph structure data, that is, select multiple graph nodes with the smallest Euclidean distance from the newly added graph node exp in the main graph structure data as neighbor graph nodes. The number of neighbor graph nodes can be custom-set. In an example, take 3 graph nodes with the smallest Euclidean distance as neighbor graph nodes. Then, establish two-way edges between the newly added graph node exp and each of its neighbor graph nodes to form a local enhanced subgraph structure with the main graph structure data.

[0039] For example, in an example, since the data volume of the entire ship propeller wake flow field is very large, only take Figure 2 the local wake flow field region of the ship propeller wake flow field as an example. The local graph representation of the main graph structure data composed of the grid nodes in this local wake flow field region is shown in Figure 2 (a). The main graph structure data in this local wake flow field region includes a total of 12 graph nodes formed by grid nodes and are represented by black circles. These 12 graph nodes formed by grid nodes are respectively denoted as s 1 to s 12. There are a total of 5 flow field scatter points in the flow field scatter point feature set located in this local wake flow field region, as shown in Figure 2 (b). Comparing Figure 2 (a) and (b) in it, it can be seen that there are connection relationships between different grid nodes, but the flow field scatter points are discrete from each other. The spatial coordinates of these 5 flow field scatter points do not coincide with the graph nodes in the main graph structure data. Therefore, these 5 flow field scatter points are all added as newly added graph nodes exp to the main graph structure data as shown in Figure 2As shown in (c) therein, these 5 graph nodes formed by the flow field scatter points are denoted as e 1 to e 5 and are represented by black diamonds.

[0040] For the graph nodes formed by the flow field scatter points e 1, based on the K-nearest neighbor strategy, search for the 3 neighbor graph nodes of graph node e 1, which are graph nodes s 8, s 9, and s 10 respectively. Then, establish two-way edges between graph node e 1 and graph nodes s 8, s 9, and s 10 respectively. For the graph nodes formed by the flow field scatter points e 2, based on the K-nearest neighbor strategy, search for the 3 neighbor graph nodes of graph node e 2, which are graph nodes s 5, s 6, and s 12 respectively. Then, establish two-way edges between graph node e 2 and graph nodes s 5, s 6, and s 12 respectively. The same processing is done for graph nodes e 3, e 4, and e 5. The schematic diagram after adding the two-way edges is as shown in Figure 2 (d) therein.

[0041] (3) Add interpolation nodes When establishing two-way edges between the graph nodes formed by the flow field scatter points and their neighbor graph nodes, these two-way edges may cross the existing two-way edges in the main graph structure data. For example, in the Figure 2 instance, the two-way edge established between graph node e 1 and its neighbor graph node s 9 crosses the two-way edge between graph nodes s 8 and s 10 in the main graph structure data.

[0042] Then, when the two-way edge a newly added between any graph node formed by the flow field scatter points and its neighbor graph node b crosses the existing two-way edge in the main graph structure data at the crossing position of the two-way edge and the two-way edge intp add a new graph node at the crossing position, and according to graph node a, graph node b , graph node c and graph node d Interpolate the respective node positions and velocity values of graph nodes intp to obtain the node position and velocity value of graph node c and graph node d are the graph nodes at both ends of the bidirectional edge . Determine the node position intp and velocity value of graph node include: First, calculate the parametric equation of the bidirectional edge a based on the node position of graph node b and the node position of its neighbor graph node . Calculate the parametric equation of the bidirectional edge c based on the node position of graph node d and the node position of graph node . Use the parametric equation of the bidirectional edge and the parametric equation of the bidirectional edge to calculate the intersection position as the node position intp of graph node , and are respectively the two coordinate values of the spatial coordinate system, which are consistent with the form of the spatial coordinates in the grid node feature set and the flow field scatter point feature set . Then, the velocity value intp at graph node can be further interpolated as:

[0043] where is the velocity value at graph node a , is the velocity value at graph node b , is the velocity value at graph node c , is the velocity value at graph node d .

[0044] For example, in the instance of Figure 2 , a new graph node e 1 and its neighbor graph node s 9, the intersection position of the bidirectional edge between them and the bidirectional edge between graph node s 8 and s 10 adds a new graph node intp denoted as i1. By calculating the parametric equations of the bidirectional edges between graph node e 1 and its neighbor graph nodes s 9, and the parametric equations of the bidirectional edges between graph node s 8 and graph node s 10, and then calculating the intersection point of the parametric equations of the two bidirectional edges, the node position of graph node i 1 can be determined. Further, by combining the velocity values of graph node e 1, graph node s 9, graph node s 8, and graph node s 10, the velocity value at graph node i 1 can be obtained. Similarly, at graph node e 2 and its neighbor graph nodes s 12, a new graph node s is added at the intersection position of the bidirectional edge between s 5 and intp denoted as i 2. At graph node e 3 and its neighbor graph nodes s 6, a new graph node s is added at the intersection position of the bidirectional edge between s 1 and intp denoted as i 3. At graph node e 5 and its neighbor graph nodes s 12, a new graph node s is added at the intersection position of the bidirectional edge between s 4 and intp denoted as i 4. The 4 new graph nodes added at the bidirectional edge intersection positions are intp each represented by a red circle.

[0045] After completing the operations in the above three stages, a unified graph structure data for virtual - real data fusion can be constructed, which can be expressed as , recording the node positions of all graph nodes, recording the velocity values at all graph nodes. recording the index information of all bidirectional edges formed by graph nodes. Through this index information, the graph nodes connected at both ends of each bidirectional edge can be determined. recording the lengths of all bidirectional edges formed by graph nodes. In the Figure 2 example, the unified graph structure data in the finally constructed local wake flow field area is as Figure 2As shown in (e) above. From the above introduction and combined with examples, it can be seen that all the graph nodes included in the finally obtained unified graph structure data mainly fall into three categories: The first category: The graph nodes formed by the grid nodes in the grid node feature set The total number of graph nodes formed by the grid nodes sim is equal to the number of grid nodes included in the grid node feature set sim . The node positions of the graph nodes formed by these grid nodes are the spatial coordinates of the corresponding grid nodes in the grid node feature set sim . The velocity values of the graph nodes formed by these grid nodes are the simulated velocities of the corresponding grid nodes in the grid node feature set sim , or are obtained by correcting the simulated velocity with the measured velocity of the flow field scatter points at the node position .

[0046] The second category: The graph nodes formed by the flow field scatter points in the flow field scatter point feature set . Since the flow field scatter points may coincide with the grid nodes, the total number exp of the graph nodes formed by the flow field scatter points exp is less than or equal to the number of flow field scatter points in the flow field scatter point feature set . The node positions of the graph nodes formed by these flow field scatter points exp are the spatial coordinates of the corresponding flow field scatter points in the flow field scatter point feature set . The velocity values of the graph nodes formed by these flow field scatter points exp are the measured velocities of the corresponding flow field scatter points in the flow field scatter point feature set .

[0047] The third category: The graph nodes inserted at the bidirectional edge crossing positions . The total number

[0047] intp of these graph nodes intp is determined according to the actual graph structure data. The node positions and velocity values intp of the graph nodes inserted at the bidirectional edge crossing positions are both calculated by the interpolation algorithm .

[0048] The graph nodes formed by the grid nodes simThose that always exist account for the majority. Since it is usually not the case that all flow field scatter points coincide with the grid nodes, there are always graph nodes formed by the flow field scatter points exp Moreover, due to the complexity of data distribution, there are often cases of two-way edge crossings, so there are graph nodes inserted at the positions of two-way edge crossings intp , so in practical applications, the finally formed unified graph structure data often includes the above three types of graph nodes at the same time, and the total number of graph nodes is .

[0049] Step S3, using the sequence composed of the unified graph structure data at any T moment and the previous M -1 nearest moments in chronological order as the sample input, and using the unified graph structure data at T +1 moment as the sample output to construct the training sample corresponding to the T moment. Construct the training samples corresponding to different moments to form a training sample set, and the integer parameter M ≥2.

[0050] Step S4, for the training sample corresponding to any T moment, use the E(n)-equivariant graph neural network model to capture the spatial structure features of the unified graph structure data at each moment in the training sample respectively and output the updated node positions and velocity features of each graph node to form the velocity field feature at the current moment.

[0051] The E(n)-equivariant graph neural network model includes multiple layers of graph convolutions for message passing in sequence. Using the E(n)-equivariant graph neural network model to capture the spatial structure features of the unified graph structure data at any moment to output the velocity field feature at that moment includes:[[]] First, initialize the first layer of graph convolution of the E(n)-equivariant graph neural network model according to the input unified graph structure data to obtain the node position j of any graph node in the unified graph structure data and the velocity feature , is the node position of graph node j in the unified graph structure data, is the node position of graph node j in the unified graph structure data, and the spatial structure feature of the first layer of graph convolution and the velocity values at each graph node are consistent with the unified graph structure data.

[0052] Then introduce the propeller rotation prior function to perform message passing from the l th layer of graph convolution to the l + 1 th layer of graph convolution. According to the lThe spatial structure features of layer graph convolution are updated to obtain graph nodes j At the l + 1 node positions in layer graph convolution and velocity features . During the message passing process of the E(n)-equivariant graph neural network model, a propeller rotation prior function is introduced, enabling the E(n)-equivariant graph neural network model to learn the translational or rotational features of the nodes in the propeller rotation region, thus ensuring its compliance with the real flow deformation in space. Among them, the propeller rotation prior function is determined according to the kinematic function and is related to the propeller rotation speed and the rotation angle of the propeller per unit time .

[0053] In one embodiment, the updated graph nodes j At the l + 1 node positions in layer graph convolution and velocity features include the following process: First, any graph node l is determined based on the node positions of each node in the j layer graph convolution, and then the adjacent graph nodes of the graph node j are calculated. Next, the message vector i between the graph node and any of its adjacent graph nodes is calculated. In this formula, i is the velocity feature of the graph node l in the layer graph convolution, j and i is the node distance between the graph node l and the graph node

[0054] in the j layer graph convolution. i Then, based on the message vector between the graph node and all its adjacent graph nodes j and combined with the propeller rotation prior function l + 1 the node position and velocity feature of the graph node

[0055] in the layer graph convolution are updated. Specifically: i where l is the node position of the graph node , is the l set of message vectors between the graph node j in the i -th layer of graph convolution and all its adjacent graph nodes.

[0056] In the above process, , and are learnable multi-layer perceptrons respectively. In one embodiment, the number of hidden layers of the multi-layer perceptron is 2, the number of hidden neurons is set to 50, and the activation function is ReLU.

[0057] Please refer to Figure 3 , taking the message passing between graph node 0 and its three adjacent graph nodes 1, 2, and 3 as an example for illustration. The node positions of graph nodes 0, 1, 2, and 3 in the l -th layer of graph convolution are as shown in Figure 3 (a), and the velocity features are successively , , , . First, calculate the message vectors to obtain , , respectively, as shown in Figure 3 (b). Then calculate the coordinate change and update the node position to . The updated node position is as shown in Figure 3 (c). Comparing with (a), it can be seen that the node position has changed, and through for feature update, the velocity features of graph nodes 0, 1, 2, and 3 in the l +1-th layer of graph convolution are successively , , , as shown in Figure 3 (d).

[0058] ​The E(n)-equivariant graph neural network model introduces a propeller rotation prior function during the message passing process, and updates the node position and velocity features simultaneously, which can dynamically capture the changes in the node spatial positions and physical laws caused by the interaction between the propeller rotation and the fluid. After successive message passing through multiple graph convolutions in the E(n)-equivariant graph neural network model, the velocity field features at that moment are obtained by synthesizing the node positions and velocity features of each graph node in the last graph convolution. The velocity field features are the learning results of the E(n)-equivariant graph neural network model for the spatial distribution of the propeller wake flow field. Through the above method, the velocity field features at each moment in a training sample can be extracted using the E(n)-equivariant graph neural network model respectively.

[0059] Step S5, input the feature time series sequence formed by the velocity field features at each moment in the training sample corresponding to the T moment in chronological order into the multi-head self-attention mechanism of the Transformer model, and obtain T the predicted value of the velocity field features at the T +1 moment as

[0060] the prediction result of the training sample corresponding to the T moment. M Input the feature time series sequence formed by the velocity field features at the moment and the previous T + 1 -1 nearest moments into the multi-head self-attention mechanism of the Transformer model to mine the temporal correlation, and predict the predicted value of the velocity field features of the ship propeller wake flow field at the

[0061] In one embodiment, the number of heads of the multi-head self-attention mechanism takes a value of 4, and the number of network layers takes a value of 2.

[0062] Step S6, use the training sample set to train the E(n)-equivariant graph neural network model and the Transformer model by combining the sample output and prediction result of each training sample, including: calculating the total loss function according to the sample output and prediction result of each training sample, and using the automatic differentiation mechanism of the neural network to adjust the model parameters of the E(n)-equivariant graph neural network model and the Transformer model according to the total loss function and performing iterative training and optimization until the model converges.

[0063] In one embodiment, the total loss function , and the four items are introduced as follows: (1) is to use the graph nodes formed by the grid nodes in the unified graph structure data simThe calculated numerical simulation data loss term, and its calculation formula is:

[0064] (2) is the graph node formed by the flow field scatter points in the unified graph structure data exp The calculated experimental scatter point supervision term, and its calculation formula is:

[0065] (3) is the newly added graph node at the intersection position of the bidirectional edges in the unified graph structure data intp The calculated interpolation node data error term, and its calculation formula is:

[0066] The above three items are respectively the data errors of three different types of graph nodes in the unified graph structure data is the velocity prediction value at the graph node j in the prediction result of the training sample is the actual velocity value at the graph node j in the sample output of this training sample. is the set composed of all graph nodes formed by grid nodes in the unified graph structure data sim is the set composed of all graph nodes formed by flow field scatter points in the unified graph structure data exp is the set composed of all newly added graph nodes at the intersection positions of all bidirectional edges in the unified graph structure data intp

[0067] (4) is the N - S physical equation regularization term calculated by using all graph nodes in the unified graph structure data combined with the N - S physical equation, and its calculation formula is:

[0068] Among them, is the number of collocation points of the N - S physical equation, and the number of collocation points can be equal to or not equal to the total number of graph nodes in the unified graph structure data. is the velocity prediction value at the graph node is the pressure value at the graph node calculated by using the velocity prediction value at the graph node combined with the N - S physical equation. is the Reynolds number, is the Laplace operator,t By encoding the NS equation as a loss function in the neural network, the pressure field can be automatically learned according to the physical formula. This is also an important role of embedding the NS equation. In the absence of the original pressure field, the pressure field can be reconstructed by inputting the velocity field data and using the NS equation.

[0069] , , are weight coefficients, which constitute a polynomial total loss function. This adjustable hyperparameter weight coefficient enables the model to achieve the best balance between multi-source data and physical laws. In one example, , , .

[0070] Step S7, after the training is completed, the model can be saved, and the trained E(n) equivariant graph neural network model combined with the Transformer model is used to predict the propeller wake field of the ship, including: Obtain the propeller wake field of the ship in the initial first ~M The flow field data of consecutive moments is collected, and the actual graph structure data of the current moment is constructed based on the flow field data of each moment. t = M At the beginning, we use the E(n) equivariant graph neural network model according to t Time and before M -1 The actual graph structure data at the most recent moment extracts the corresponding velocity field features, and t Time and before M -1 The velocity field features extracted at the most recent moment are input into the multi-head self-attention mechanism of the Transformer model in a time sequence sequence. t +1 time velocity field characteristic prediction value. Then we can continue to perform autoregressive forecasting, that is, according to t Construction of velocity field characteristic prediction value at time +1 t +1 time point actual graph structure data, then let t = t +1 and repeat the above process to continue to obtain the forecast result of the flow field data at the next moment, and the cycle is repeated to realize the autoregressive forecast.

[0071] The above is only a preferred embodiment of the present application, and the present application is not limited to the above embodiments. It is understood that other improvements and changes directly derived or associated by those skilled in the art without departing from the spirit and concept of the present application should be considered to be included in the protection scope of the present application.

Claims

1. A method for predicting the propeller flow field using a spatio-temporal graph neural network with virtual-real data fusion, characterized in that, The method for predicting the propeller flow field by the spatio-temporal graph neural network includes: Construct a set of grid node features at any moment using the numerical simulation data of the wake flow field of a ship's propeller , and construct a set of flow field scatter point features at any moment using the physical test measurement data of the wake flow field of a ship's propeller ; among them, the set of grid node features at each moment includes the spatial structure features between grid nodes and the simulated velocity at the current moment of the spatial coordinates of each grid node, and the set of flow field scatter point features at each moment includes the spatial coordinates of each flow field scatter point and the measured velocity at the current moment of each flow field scatter point; Adopt the feature set of each grid node Construct the main graph structure data, and establish the feature set of flow field scatter points at the current moment based on the K-nearest neighbor strategy The local enhanced subgraph structure between the main graph structure data to obtain the unified graph structure data of virtual-real data fusion at the current moment. There is a corresponding speed value at each graph node in the unified graph structure data; At any T time and before M -1 sequences of unified graph structure data at the nearest times in chronological order are used as sample inputs, and T the unified graph structure data at the +1 time is used as the sample output to construct T the training samples corresponding to the time. The training samples corresponding to different times are constructed to form a training sample set, and the integer parameter M ≥2; For any T training sample corresponding to a moment, use the E(n)-equivariant graph neural network model to capture the spatial structure features of the unified graph structure data at each moment in the training sample respectively, and output the updated node positions and velocity features of each graph node to form the velocity field feature at the current moment; input the feature time series sequence formed by the velocity field features at each moment in the training sample in chronological order into the multi-head self-attention mechanism of the Transformer model, and obtain T the predicted value of the velocity field feature at the +1 moment as T the prediction result of the training sample corresponding to the moment; Combining the sample output and prediction result of each training sample, using the training sample set to train the E(n)-equivariant graph neural network model and the Transformer model, and using the trained E(n)-equivariant graph neural network model and Transformer model to predict the wake flow field of the ship propeller.

2. The method for predicting the propeller flow field by the spatio-temporal graph neural network according to claim 1, wherein Using the E(n)-equivariant graph neural network model to output the velocity field features at each moment includes: Initialize the first-layer graph convolution of the E(n)-equivariant graph neural network model according to the input unified graph structure data to obtain any graph node in the unified graph structure data j At the node position of the first-layer graph convolution And the velocity feature , Is the graph node j The node position in the unified graph structure data Is the graph node j The velocity value in the unified graph structure data Introduce the propeller rotation prior function to perform message passing from the l -th layer of graph convolution to the l + 1 -th layer of graph convolution, and update the graph nodes according to the spatial structure features of the l -th layer of graph convolution to obtain the graph nodes j At the node positions l + 1 in the -th layer of graph convolution and the velocity features ; Integrating the node positions and velocity features of each graph node in the last layer of graph convolution to obtain the velocity field features at the current moment.

3. The method for predicting the propeller flow field by the spatio-temporal graph neural network according to claim 2, wherein Update to obtain graph nodes j At the l + 1 Node positions in the layer graph convolution and velocity features Include: According to the l node positions of each node in the j layer graph convolution, determine any graph node j adjacent graph nodes, and calculate the graph node i and any adjacent graph node the message vector between them, where is the velocity feature of the graph node i in the l layer graph convolution, is the node distance between the graph node j and the graph node i in the l layer graph convolution, is a learnable multi-layer perceptron; According to the graph node j and all its adjacent graph nodes i the message vector between them combines with the propeller rotation prior function to update and obtain the graph node j at the l + 1 layer graph convolution node position and velocity feature ; among them, the propeller rotation prior function is determined according to the kinematic function and is related to the propeller rotation speed and the rotation angle of the propeller per unit time related.

4. The method for predicting the propeller flow field by the spatio-temporal graph neural network according to claim 3, wherein Update to obtain graph nodes j At the l + 1 Node positions in the -th layer of graph convolution And velocity features Are as follows: Among them, is the node position in the i th l layer of graph convolution, , is the l th layer of graph convolution, and the set of message vectors j formed between the graph node i and all its adjacent graph nodes . and are learnable multi-layer perceptrons respectively.

5. The method for predicting the propeller flow field by the spatio-temporal graph neural network according to claim 1, wherein, Obtaining the unified graph structure data of the current virtual-real data fusion includes: The set of grid node features at the current moment Each grid node in it is used as a graph node in the main graph structure data sim The connections between grid nodes form the corresponding graph nodes in the main graph structure data sim The bidirectional edges between them to construct the main graph structure data at the current moment, and the spatial coordinates of each grid node are used as the node positions of the corresponding graph nodes in the main graph structure data sim The simulated speed at the grid node is used as the speed value at the corresponding graph node sim ;​​ For the set of flow field scatter point features at the current moment For any one of the flow field scatter points in it, when the spatial coordinates of the flow field scatter point coincide with the node positions of the graph nodes formed by the grid nodes in the main graph structure data sim the measured velocity at the flow field scatter point is used to correct the velocity value at the coincident graph node sim to, where the fusion weight coefficient is ; ​ When the spatial coordinates of the flow field scatter points do not coincide with the node positions of all the graph nodes in the main graph structure data, the flow field scatter points are used as newly added graph nodes exp and the spatial coordinates of the flow field scatter points are used as the node positions of the corresponding newly added graph nodes exp . The measured velocity at the flow field scatter points is used as the velocity value at the corresponding newly added graph nodes exp . Based on the K-nearest neighbor strategy, search for the neighbor graph nodes of the newly added graph nodes in the main graph structure data, and respectively establish bidirectional edges between the newly added graph nodes exp and each of their neighbor graph nodes to form a local enhanced subgraph structure with the main graph structure data. exp ​ 6. The spatio-temporal graph neural network propeller flow field prediction method according to claim 5, characterized in that Obtaining the unified graph structure data of the current virtual-real data fusion also includes: When a new graph node is added at any scatter point in the flow field a and the graph nodes of its neighbors b a two-way edge is established between them and the existing two-way edges in the main graph structure data when they cross, at the crossing position of the two-way edge and the two-way edge a new graph node is added intp and the node position and velocity value of the graph node a the graph node b the graph node c and the graph node d are used to interpolate the node position and velocity value of the graph node intp wherein, the graph node c and the graph node d are the graph nodes at both ends of the two-way edge .

7. The method for predicting the propeller flow field of the spatio-temporal graph neural network according to claim 6, characterized in that Interpolate to obtain the graph nodes intp The node positions and velocity values include: According to the node positions of the graph nodes a and the node positions of the neighbor graph nodes b calculate the parametric equations of the bidirectional edges According to the node positions of the graph nodes c and the node positions of the graph nodes d calculate the parametric equations of the bidirectional edges Utilize the parametric equations of the bidirectional edge and the parametric equations of the bidirectional edge to calculate the intersection position as the node position of the graph node intp ; ; Interpolate to determine the velocity value at the graph node intp is as follows: Among them, is the speed value at graph node a . is the speed value at graph node b . is the speed value at graph node c . is the speed value at graph node d .

8. The method for predicting the propeller flow field by the spatio-temporal graph neural network according to claim 6, wherein The unified graph structure data includes graph nodes formed by grid nodes sim , graph nodes formed by flow field scatter points exp , and graph nodes newly added at the positions of bidirectional edge intersections intp ; The method for predicting the propeller flow field by the spatio-temporal graph neural network further includes: The neural network automatic differentiation mechanism is adopted to perform model training according to the total loss function ; among them, ; where is the numerical simulation data loss term calculated using the graph nodes formed by the grid nodes in the unified graph structure data sim , is the experimental scatter point supervision term calculated using the graph nodes formed by the flow field scatter points in the unified graph structure data exp , is the interpolation node data error term calculated using the graph nodes newly added at the intersection positions of the bidirectional edges in the unified graph structure data intp , is the N-S physical equation regularization term calculated using all the graph nodes in the unified graph structure data in combination with the N-S physical equation; , , are the weight coefficients respectively.

9. The method for predicting the propeller flow field by the spatio-temporal graph neural network according to claim 8, wherein Total loss function The calculation formulas for each item in it are as follows: Among them, is the predicted velocity value at the graph node j in the prediction result of the training sample, is the actual velocity value at the graph node j in the sample output of the training sample; is the set composed of all graph nodes formed by grid nodes in the unified graph structure data sim ; is the set composed of all graph nodes formed by flow field scatter points in the unified graph structure data exp ; is the set composed of newly added graph nodes at the cross positions of all bidirectional edges in the unified graph structure data intp ; is the number of collocation points of the N - S physical equation, is the predicted velocity value at the graph node ; is the pressure value at the graph node calculated by combining the predicted velocity value at the graph node with the N - S physical equation; is the Reynolds number, is the Laplace operator.

10. The method for predicting the propeller flow field by the spatio-temporal graph neural network according to claim 1, wherein, Using the trained E(n)-equivariant graph neural network model combined with the Transformer model to predict the wake flow field of the ship propeller includes: Obtain the flow field data of the ship propeller wake field at the initial first ~M consecutive moments, and construct the actual graph structure data at the current moment according to the flow field data at each moment; From t = M the start, using the E(n) equivariant graph neural network model, respectively extract the corresponding velocity field features according to the actual graph structure data at the t moment and the previous M -1 nearest moments, and input the feature time series sequence formed by the velocity field features extracted at the t moment and the previous M -1 nearest moments in chronological order into the multi-head self-attention mechanism of the Transformer model to obtain the predicted value of the velocity field feature at the t +1 moment and perform autoregressive forecasting.

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