Pump-jet propeller fluid-structure interaction digital twinning method based on message passing graph neural network

Abstract

The invention discloses a pump-jet propeller fluid-structure interaction digital twinning method based on a message passing graph neural network, and belongs to the technical field of fluid machinery intelligent design and digital twinning. The method mainly comprises the following steps: constructing an adjustable geometric model of the pump-jet propeller; generating a multi-physical field simulation data set by adopting uniform sampling or Latin hypercube sampling; characterizing the fluid-structure interaction multi-physics field as graph structure data, and realizing efficient prediction of the multi-physics field in different geometric forms by using a deep message passing graph neural network; s4, realizing efficient training of large-scale graph data through a sub-graph clustering and blocking strategy; and S5, based on three-dimensional visualization and computer graphics technologies, constructing an interactive pump-jet propeller digital twinborn visualization platform under a B / S architecture, and realizing parameter adjustment, real-time simulation and dynamic visualization. According to the method, the modeling efficiency and the prediction precision of the pump jet propeller under the complex variable geometry working condition are remarkably improved, and the method can be widely applied to design and performance evaluation of an underwater vehicle propulsion system.

Description

Technical Field

[0001] This invention belongs to the field of intelligent design and digital twin technology of fluid machinery, specifically relating to a digital twin method for fluid-structure interaction of pump-jet propulsion based on message-passing graph neural network. Background Technology

[0002] Pump-jet propulsion, as the core power unit of modern underwater vehicles, directly determines the vehicle's speed, stealth capabilities, and endurance. Traditional design processes rely on coupled computational fluid dynamics (CFD) and finite element method (FEM) simulations, iterating repeatedly on parameters such as blade geometry, pitch, and chord length to optimize propulsion efficiency and reduce cavitation noise. However, as underwater equipment evolves towards higher speeds, quieter operation, and multi-condition adaptive design, the design space expands exponentially, making it difficult to meet the demands of rapid iteration.

[0003] Traditional pump-jet propulsion design relies on computational fluid dynamics (CFD) and fluid-structure interaction (FSI) simulation techniques, which present significant bottlenecks. Traditional CFD methods require repeated generation of structured meshes for varying geometric parameters, resulting in computation times ranging from hours to days, making them unsuitable for dynamic geometric optimization. Existing parametric modeling tools lack flexibility for complex geometric deformations (such as blades with non-uniform curvature), and mesh mismatch and interface propagation errors in FSI simulations lead to decreased accuracy in multiphysics predictions. While deep learning models (such as convolutional neural networks and long short-term memory networks) have been introduced for flow field prediction, they rely on structured and sequential data. Existing graph neural network solutions suffer from high computational complexity and memory consumption when directly processing large-scale unstructured meshes, hindering efficient training and deployment. Furthermore, traditional visualization platforms rely on local high-performance hardware and cannot support real-time interaction and cross-platform collaboration through lightweight web interfaces, limiting design iteration efficiency.

[0004] To address the aforementioned issues, there is an urgent need for a panoramic digital twin platform that integrates geometric parametric modeling, physical constraint graph learning, and real-time visualization interaction, in order to overcome industry bottlenecks such as poor dynamic geometric adaptability, low accuracy of multi-field coupling, and limited engineering deployment efficiency. Summary of the Invention

[0005] In view of the shortcomings of existing technologies, this application provides a digital twin method for fluid-structure interaction (FSI) of pump-jet propulsion based on message-passing graph neural networks, aiming to solve the core problems existing in traditional pump-jet propulsion design, such as poor dynamic geometry adaptability, low efficiency of multi-physics coupling simulation, insufficient physical consistency of data-driven models, and weak real-time visualization and interaction. This invention can achieve efficient modeling, high-precision prediction, and real-time interactive analysis in fluid-structure interaction scenarios with varying geometry.

[0006] The technical means employed in this invention are as follows: A digital twin method for fluid-structure interaction of pump-jet propulsion based on message-passing graph neural networks includes the following steps: S1. Based on the selection of geometric parameters and inverse parameterization modeling of the blade spatial stacking law, an adjustable geometric model of the pump-jet propulsion system is constructed. S2. Under the automated solution framework, uniform sampling or Latin hypercube sampling is used to generate a fluid-structure interaction multiphysics simulation dataset. The fluid-structure interaction multiphysics includes grid node physical quantities and element physical quantities, wherein the element physical quantities include the stress inside the pump impeller element. S3. The fluid-structure interaction multiphysics field attached to the grid nodes and units is characterized as graph structure data, and a deep message passing graph neural network is constructed. The deep message passing graph neural network is used to output the corresponding fluid-structure interaction multiphysics field quantities based on the graph structure data with different geometric shapes input, including the flow field, structural field physical quantities and stress inside the pump impeller unit corresponding to the grid node. S4. Implement large-scale graph data training for deep message-passing graph neural networks through subgraph clustering and block segmentation strategies; S5. Based on 3D visualization and computer graphics technology, an interactive pump-jet propulsion digital twin visualization platform under B / S architecture is constructed to realize parameter adjustment, real-time simulation and dynamic visualization.

[0007] Furthermore, in S1, the selection of geometric parameters based on the spatial stacking law of the blade includes: selecting the blade profile shape characteristics and blade spatial stacking parameters as the parameterization index of the propeller blade. The blade profile shape characteristics include chord length, thickness, camber and the position of maximum camber. The blade spatial stacking parameters include pitch, longitudinal tilt and skew. Inverse parametric modeling includes: using B-spline fitting to fit the spatial stacking parameters of the thruster blades, performing parametric fitting via Python to convert the 3D geometric model into a parametric model, and then using AutoGrid5 in NUMECA. TM Generate the corresponding parametric geometric structured mesh.

[0008] Furthermore, in S2, under the automated solution framework, uniform sampling or Latin hypercube sampling is used to generate a fluid-structure interaction multiphysics simulation dataset, including: The simulation is automated in batches using Python and ANSYS Workbench's CS mode. The fluid-structure interaction results of each sample are stored as an unstructured field dataset in the form of nodes and elements. Determined based on numerical simulation Design variables The geometric parameters are obtained by selecting them through uniform sampling or Latin hypercube sampling. For each sample point, the pump spray mesh under the corresponding geometric parameters is obtained through the inverse parameterization modeling method. Then, the key physical quantities of the sample response value are solved by numerical simulation based on simulation verification. Based on ANSYS workbench and Client-Server mode, Python drives the automated updating of the structured mesh generated by NUMECA, and outputs saved physical field mesh information and calculation results.

[0009] Furthermore, in S3, the fluid-structure interaction multiphysics fields attached to mesh nodes and elements are characterized as graph-structured data, including: Define vector It is a collection containing the indices of three-dimensional mesh nodes, a matrix It is an adjacency matrix describing the connections between nodes, and ; Encode the relative displacement of two nodes in the grid space as And convert the relative displacement into mesh edge features. ;in, Indicates relative displacement. express Node coordinates express Node coordinates Indicates spatial dimension, By collecting edge features, the corresponding feature matrix is ​​obtained. in , Indicates the total number of grid nodes. It is the stress embedded inside the pump impeller unit, which serves as the element feature and edge feature matrix. Connections, together constituting the core physical characteristics of a graph structure, define the input graph of a deep message-passing graph neural network as... , where the input matrix The Behavior ,in For related Geometric parameters, To design the variable dimensions, the output graph is defined as follows: The output matrix The Behavior ,in It includes A snapshot of the flow of interest for the physical quantity. For the types of flow field parameters, The structural field parameters are types, including those related to element characteristics. Statistical characteristics of the internal stress of the corresponding pump impeller unit.

[0010] Furthermore, in S3, the deep message-passing graph neural network includes node encoders, edge encoders, message-passing processors, aggregation processors, and node decoders; among which, the message-passing processor... Used to update edge features, through the adjacency matrix. To visit via the border Connect to node nodes ,Right now ; Aggregator First, use the operator. For nodes Connected edges Summation, then solving for aggregated features. :

[0011] pass and The MP aggregation operation will be repeated Next, implement based on In deep structures, message passing strategies gradually expand the neighborhood under consideration to capture features at different scales.

[0012] Furthermore, in S4, large-scale graph data training for deep message-passing graph neural networks is achieved through subgraph clustering and block-splitting strategies. This includes using a random multi-clustering strategy for subgraph splitting to divide the original large-scale graph into several subgraph clusters, and then training in parallel through a cluster-GCN structure.

[0013] Furthermore, in S4, the training of large-scale graph data for deep message-passing graph neural networks is achieved through subgraph clustering and block-based strategies, and also includes: Input image Divided into Each cluster is randomly selected in each batch during model training. Sub-atlas This results in a merged graph. Its corresponding adjacency matrix is:

[0014] in At this point, the number of edges is The overall time complexity of cluster-GCN is .

[0015] Furthermore, based on 3D visualization and computer graphics technologies, an interactive pump-jet propulsion digital twin visualization platform under a B / S architecture is constructed, including: A pre-trained deep message-passing graph neural network is loaded using a server program written in Python. The program receives geometric parameters input by the user and calls the deep message-passing graph neural network in real time to perform multiphysics prediction and generate flow field and structural field data. A dynamic web interface is built based on the Trame framework, integrating parameter input controls and a 3D visualization window, allowing users to adjust geometric parameters online and trigger simulation calculations. Utilize the VTK engine for efficient rendering of unstructured mesh data.

[0016] Furthermore, based on 3D visualization and computer graphics technologies, an interactive pump-jet propulsion digital twin visualization platform under a B / S architecture is constructed, which also includes: Through standardized API interfaces, the interactive pump-jet propulsion digital twin visualization platform can interact with external CFD software and industrial IoT platforms to achieve cross-platform collaborative simulation and multi-source data fusion.

[0017] Compared with the prior art, the present invention has the following advantages: 1. This invention uses decoupling modeling of geometric parameters and mesh topology to avoid the repetitive mesh generation caused by geometric changes in traditional CFD.

[0018] 2. This invention captures the multi-scale features of complex multi-physics fields during deep message passing, thereby achieving high-precision prediction of multi-physics fields in pump-jet propulsion systems under fluid-structure interaction.

[0019] 3. This invention is based on a subgraph clustering strategy, which enables controllable memory usage for model training and supports distributed training of millions of unstructured grid nodes; 4. This invention achieves second-level response for parameter adjustment to physical field visualization through lightweight web services, is compatible with mainstream browsers and mobile terminals, and lowers the hardware deployment threshold.

[0020] 5. The system has good scalability and cross-platform compatibility, and can be seamlessly integrated with industrial design and simulation software. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a flowchart of the panoramic digital twin method for pump-jet propulsion based on message-passing graph neural network in an embodiment of the present invention.

[0023] Figure 2 This is a schematic diagram of a pump-jet propulsion unit with a front stator in an embodiment of the present invention.

[0024] Figure 3 This is a schematic diagram illustrating the cumulative parameters of the pump impeller pitch and chord length in an embodiment of the present invention.

[0025] Figure 4 This is a schematic diagram of the message passing graph neural network established in an embodiment of the present invention.

[0026] Figure 5 The rotor blade stress field predicted by the message passing graph neural network in this embodiment of the invention (geometric deformation magnified 10,000 times).

[0027] Figure 6 The interface of the pump-jet fluid-structure interaction digital platform version 1.0 in this embodiment of the invention. Detailed Implementation

[0028] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0029] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0030] This invention provides a digital twin method for fluid-structure interaction of pump-jet propulsion based on message-passing graph neural networks, comprising the following steps. S1. Based on the selection of geometric parameters and inverse parameterization modeling of the blade spatial stacking law, an adjustable geometric model of the pump-jet propulsion system is constructed.

[0031] Specifically, the geometric parameters selected in this application include propeller blade parametric indices and blade spatial stacking parameters. The propeller blade parametric indices include blade profile characteristics such as chord length, thickness, camber, and the location of maximum camber. The blade spatial stacking parameters include pitch, tilt, and skew. Inverse parametric modeling uses B-spline fitting to fit the spatial stacking parameters of the propeller blades. Parametric fitting is performed using Python to convert the 3D geometric model into a parametric model. By adjusting the B-spline control points and blade shape distribution parameters, flexible reconstruction of the geometry is achieved, and the model is then implemented using AutoGrid5 in NUMECA. TM Generate a high-quality structured mesh for the geometry under the corresponding parameterization.

[0032] S2. Under the framework of automated solution, uniform sampling or Latin hypercube sampling is used to generate a fluid-structure interaction multiphysics simulation dataset.

[0033] Specifically, automated batch simulation calculations are achieved using Python and ANSYS Workbench's client-server (CS) mode, storing the fluid-structure interaction (FSI) results of each sample as an unstructured field dataset in the form of nodes and elements. This is determined from numerical simulations in fluid mechanics and FSI. Design variables And obtain geometric parameters by selecting them through uniform sampling or Latin hypercube sampling. For each sample point, the pump-jet mesh under the corresponding geometric parameters is obtained through inverse parametric modeling. Then, the key physical quantities of the sample response values ​​are solved using existing numerical simulation based on simulation verification. Based on ANSYS Workbench and Client-Server (CS) mode, the structured mesh generated by NUMECA is automatically updated via Python, and the physical field mesh information and calculation results are output and saved.

[0034] Design variables The determination of the target needs to be combined with physical mechanisms, simulation sensitivity analysis and engineering constraints. The specific steps include preliminary screening of physical mechanisms, simulation sensitivity analysis and limiting the scope by engineering constraints.

[0035] Preliminary screening of physical mechanisms: Prioritize geometric parameters that have a significant impact on propeller performance (thrust, efficiency, stress), including blade profile characteristics (chord length, thickness, camber, maximum camber position) and blade spatial stacking parameters (pitch, roll, skew).

[0036] Simulation sensitivity analysis: A coupled simulation platform was built using ANSYS CFX / ABAQUES. The influence of parameters was quantified using the control variable method, and highly sensitive parameters (such as the pitch control point in the example) were retained. chord length control point ).

[0037] Engineering constraints limit the range of parameter values: Based on manufacturing process tolerances and thruster operating requirements, the range of parameter values ​​is determined (as shown in the example). , ).

[0038] S3. The fluid-structure interaction (FSI) multiphysics fields attached to the grid nodes and elements are represented as graph structure data, and a deep message-passing graph neural network is constructed. The deep message-passing graph neural network is used to output the corresponding FSI multiphysics quantities based on the graph structure data with different geometric shapes as input.

[0039] The deep message-passing graph neural network in this application includes a coordinate encoder, a node encoder, an edge encoder, a message-passing processor, an aggregation processor, and a node decoder; wherein, the message-passing processor aggregates the neighborhood features of nodes based on the adjacency matrix to achieve joint updates of local topology and physical quantities.

[0040] In this step, the simulation nodes are preprocessed into a graph format. First, vectors are defined. It is a collection containing the indices of three-dimensional mesh nodes. (Matrix) This is an adjacency matrix describing the connections between nodes. It's important to note here that... This is because the edges between nodes are bidirectional. Furthermore, positional features are provided as relative edge features to achieve spatial isotropy. The relative displacement of two nodes in the mesh space is encoded as... , where coordinates and standardize it. Convert to mesh edge features By collecting edge features, the corresponding feature matrix is ​​obtained. in , It is the stress embedded inside the pump impeller unit.

[0041] In this step, the multiphysics fields attached to the mesh nodes and cells are used for graph learning, including defining the input graph. , where the input matrix The Behavior ,in For related Geometric parameters. Similarly, the input graph of a deep message-passing graph neural network is defined as... , where the input matrix The Behavior ,in For related Geometric parameters, To design the variable dimensions, the output graph is defined as follows: The output matrix The Behavior ,in It includes A snapshot of the flow of interest for the physical quantity. For the types of flow field parameters, The structural field parameters are types, including those related to element characteristics. Statistical characteristics of the internal stress of the corresponding pump impeller unit.

[0042] Furthermore, the pump-jet multiphysics prediction task in this step is defined as: given a pair of and , graph simulator Learning nonlinear mappings This is achieved through well-known depth map convolution modules, etc.

[0043] Here, a depth graph convolutional module is used as the deep message-passing graph neural network in this application, adopting an "encoder-processor-decoder" architecture. The specific composition and implementation are as follows: Module composition: includes a coordinate encoder. Node encoder Side encoder Message passing processor Aggregator Node decoder and stress decoder Through the encoder layer Node features Mapping to a higher-dimensional latent space (input dimension) Output dimension ), opposite edge features The same encoding is performed; the processors are layered by message-passing processors. Through the adjacency matrix Update edge embedding ( ), Aggregate neighborhood feature update node embedding ( ), iteration Layers; decoder layers consist of Output flow field + structure field physical quantities Output unit stress Clustering by subgraph (divided into) The time complexity is optimized to [number of subgraphs] and parallel training with cluster-GCN. It supports training on millions of nodes.

[0044] Generally speaking, Layer GCN adopts Graph convolution operations derive node embeddings progressively from low to high layers. For the ... Layers, nodes The embedding is achieved by capturing the matrix It is obtained by defining the embedding of its neighboring nodes:

[0045] Among them, operators Represents aggregate functions, and This represents a differentiable nonlinear mapping function, which can be implemented using a multilayer perceptron, etc. The model includes: (a) a coordinate encoder. (b) Node encoder (c) Side encoder (d) Message passing processor (e) Aggregation processor (f) Node decoder The encoder uses geometric parameters and initial geometric coordinates Nodes and edge embeddings are generated using features, and then the processor is responsible for aggregating the cluster nodes. and grid edges The encoder first extracts features and then updates them. Finally, the decoder performs post-processing to provide the final prediction result. and Its function is to generate node and edge embeddings by mapping the features of the input graph to a high-dimensional latent space. That is...

[0046]

[0047] The outputs of the two encoders have the same feature dimension, so the processor can perform matrix concatenation along the feature dimension.

[0048] This application utilizes a deep message-passing graph neural network to achieve multiphysics prediction of pump-jet under variable geometry. Firstly, it utilizes an additional coordinate encoder (represented as...). To predict geometric parameters Related node coordinates Traditional methods often require regenerating the mesh whenever geometric parameters change, which is not only computationally expensive but also challenging, especially when dealing with previously unseen geometric parameters. Specifically, regarding geometric parameters... Corresponding coordinates It is determined by the initial node coordinates of the numerical model. The original export, i.e.

[0049] This coordinate encoder eliminates the need for mesh information (including nodes and edges) associated with geometric parameters. Because it does not require current mesh information, the coordinate encoder has an advantage in predicting unknown geometric parameters by decoupling the geometric parameters from the generated mesh.

[0050] Message passing processor Used to update edge features. That is, through the adjacency matrix. To visit via the border Connect to node nodes ,Right now

[0051] In addition, aggregate processor It involves two steps. First, it uses operators. For nodes Connected edges Summation. Then, aggregate the features. With node embedding merged into

[0052] Among them, through and The MP aggregation operation will be repeated Next, that is, based on Layered message passing layer. In this deep structure, the message passing strategy progressively expands the considered neighborhood to capture features at different scales. Finally, through... The updated node features are passed to the decoder. and To output the prediction results, i.e.

[0053]

[0054] S4. Implement large-scale graph data training for deep message-passing graph neural networks through subgraph clustering and block segmentation strategies.

[0055] Specifically, this application employs a random multi-clustering strategy for subgraph splitting, dividing the original large-scale graph into several subgraph clusters. Parallel training using a cluster-GCN structure reduces the computational complexity of global feature aggregation. This application utilizes subgraph splitting operations to achieve feature clustering, narrowing the global cross-scale range and reducing the difficulty of aggregating local features. It adopts a "divide and conquer" strategy to achieve efficient learning of large-scale flow graphs, thereby extracting local features. Input graph nodes Classified as Group ,in and By the It consists of nodes in each partition. Simultaneously, a graph clustering algorithm is used to analyze the graph. The goal of partitioning is to maximize the number of edges retained. This method captures the clustering and community structure of the graph. The subgraph is divided into:

[0056] in ,matrix Depend on The links between nodes form the graph. Similarly, the output graph... Cut into After reorganizing the nodes, the adjacency matrix... Classified as Submatrix, i.e.

[0057] in and

[0058] As can be seen, large adjacency matrix Approximated by its diagonal blocks The graph replaces the previous one. It shows the neighborhood expansion of a clustered graph. Graph clustering avoids extensive neighborhood searches, focusing only on the neighborhood within a cluster. Nodes in the cluster do not need to perform extensive neighborhood searches. Perform a neighborhood search outside of the area.

[0059] Feature clustering through subgraph splitting can also reduce the computational burden of directly processing large-scale simulation data during the training process. Specifically, when dividing a graph into independent subgraphs, features are deleted... Partial. Therefore, a random multi-clustering strategy was adopted to connect clusters and minimize the variance between different batches. Specifically, the figure Classified as A cluster, relatively large This value ensures the breadth of cluster diversity. During model training, each batch randomly selects one... Sub-atlas Instead of focusing on just one cluster, this produces a merged graph. Its corresponding adjacency matrix is:

[0060] in .matrix In fact The submatrix. At this point, the number of edges is... The overall time complexity of the cluster-GCN is... In terms of space complexity, only loading... Subgraphs, therefore only Memory is used to store the embedded data.

[0061] Quantization compression and operator fusion are performed using a graph neural network model, and the inference process is accelerated by GPUs, ensuring that the time for a single prediction is less than 500ms (more than 50 times more efficient than traditional CFD simulation). The backend service is deployed on a GPU cluster, using CUDA to accelerate the VTK rendering pipeline and graph model inference, supporting high-concurrency user access and large-scale data throughput.

[0062] S5. Based on 3D visualization and computer graphics technology, an interactive pump-jet propulsion digital twin visualization platform under B / S architecture is constructed to realize parameter adjustment, real-time simulation and dynamic visualization.

[0063] This project utilizes 3D visualization technology and computer graphics to achieve interactive visualization of high-dimensional physical fields in pump-jet propulsion systems. Specifically, it includes: constructing a fluid-structure interaction prediction platform for pump-jet propulsion systems using a B / S (browser / server) architecture; and developing an interactive 3D visualization service for unstructured mesh data based on the Trame web framework and the VTK visualization toolkit. The backend service involves a Python server-side program that loads a pre-trained graph neural network model, receives user-input geometric parameters such as blade chord length, pitch, and B-spline control points, and calls a deep message-passing graph neural network in real time for multi-physics prediction, generating flow field (velocity, pressure) and structural field data. A dynamic web interface is built based on the Trame framework, integrating parameter input controls (such as sliders and forms) with a 3D visualization window, allowing users to adjust geometric parameters online and trigger simulation calculations. The VTK engine is used for efficient rendering of unstructured mesh data.

[0064] This application enables dynamic interaction and real-time simulation of high-dimensional physical fields in pump injection. Users first modify the geometric parameters defined in step S1 (such as B-spline control points and blade stacking parameters) through a web interface. The backend automatically generates new geometry based on an inverse parameterized model and predicts the corresponding physical field using a graph neural network. The results are fed back to the front-end VTK window in real time, forming a closed loop of "parameter adjustment - model prediction - visualization update". This application's solution supports synchronous or independent visualization of the flow field (pressure contour map, velocity vector) and the structural field (stress distribution, deformation displacement), and employs color mapping, dynamic scales, and cross-sectional analysis tools to enhance data interpretability.

[0065] Based on the above methods, a platform-based encapsulation can be performed to build a digital twin platform. This platform provides standardized API interfaces, supports data interaction with external CFD software and industrial IoT platforms, and enables cross-platform collaborative simulation and multi-source data fusion. It supports multi-scale visualization from macroscopic overall flow fields to microscopic local stress gradients of blades. It can also combine a subgraph splitting strategy to load high-precision physical field data of local areas on demand, balancing rendering performance and detail display requirements.

[0066] This application utilizes an automated framework (Python + ANSYS CS mode) to perform batch simulations of multiple geometric conditions, outputting complete data of "geometric parameters - flow field - structural field" as training samples for the GNN model (e.g., 36 samples in the example); dynamic geometric adaptability improvement: through inverse parameterization + B-spline fitting, the 3D geometric model is transformed into a parameterized model, combined with a coordinate encoder. This achieves decoupling of geometric parameters from mesh topology, allowing adaptation to new geometries without regenerating the mesh. Furthermore, the constructed deep message-passing GNN model, trained on existing simulation data, achieves a single inference time of only 85 seconds after training (Table 3), a 200+ times improvement in efficiency compared to traditional CFD simulation (17579 seconds). Prediction accuracy is guaranteed: through subgraph clustering and L-layer message passing, multi-scale coupling features are captured, with a relative error of <2% (Table 2), solving the interface transmission error problem of traditional simulations.

[0067] The following description, in conjunction with the accompanying drawings, further illustrates the scheme and effects of this application.

[0068] The embodiments of the present invention include multiple steps, such as Figure 1 As shown, the offline stage is Figure 1 The dashed arrows indicate the data generation process. Considering that data simulation itself is very time-consuming, this process can be performed separately or existing data can be used directly. The specific process is as follows: First, a simulation template is constructed. In this embodiment, the template selected is as follows: Figure 2 The pump-jet propulsion model shown has a front-stator design comprising 13 stator blades and 9 rotor blades. The rotor diameter for the pump-jet propulsion is... The chord length (at 70% radius) is 24% of the diameter, the pitch ratio is 1.10, and the rotational speed is set to... In this embodiment, for accurate numerical simulation, the entire computational domain is divided into three parts: the rotor domain, the stator domain, and the external open water domain. High-quality hexahedral meshes are generated using NUMECA AutoGrid5TM for the stator and rotor parts, with a mesh element count of 6.1 × 10⁻⁶. 6 and 4.8×10 6 The outer watershed mesh was generated using Ansys ICEM, with a total of 9.0 × 103 elements. 6In the fluid-structure interaction computational mesh modeling, Ansys ICEM structured mesh software was used to mesh the blades to ensure that the topological relationship of the generated blade structured mesh remains unchanged when the blade geometry changes, i.e., the number of mesh nodes is consistent with the topological connection relationship. Local refinement was performed at the blade leading edge, trailing edge, blade root, and blade tip to capture stress concentration phenomena. The finite element computational mesh model has 92,140 elements and 84,208 nodes.

[0069] Then, the experimental design was implemented, namely S1, from the design process of the underwater vehicle pump-jet propulsion system, the selection of parameterized indicators for the pump-jet blades was determined, and inverse parameterized modeling under geometric parameter control was achieved; As shown in Figure 3, pitch angle chord length Selected as a geometric variable, its radial distribution is defined by a B-spline curve with three control points:

[0070] Among them, for B-spline basis functions for:

[0071] Control Points , and For curve shaping, basis functions ensure continuity and curve smoothness. In this embodiment, the pump impeller pitch angle control point... The range of variation is [0.35, 0.50], chord length control point. The range of variation is [0.045, 0.05].

[0072] Secondly, the database is generated, mainly relying on S3. Under the automated solution framework, it is obtained through experimental design methods such as uniform sampling or Latin hypercube sampling. Numerical simulation techniques such as computational fluid dynamics and fluid-structure interaction are implemented in batches to obtain datasets. According to the selected and ,use Figure 3 (c) Uniform sampling was performed, and CFD and FEM calculations were conducted to obtain data for 36 cases.

[0073] Next, a proxy model, namely S3, is built to represent the multiphysics fields attached to the grid nodes and cells as graph data format, and the pump spray multiphysics fields under variable geometry are predicted based on a deep message-passing graph neural network.

[0074] Table 1. Detailed parameters of the message passing graph model, where The average number of nodes in each batch of clustered subgraphs. Let be the number of edges in the subgraph. To hide the dimension, finally L MP layer number

[0075] Table 1 lists the detailed implementation process of each component of the message passing graph model implemented using MLP. To efficiently train the model, we first sample a subset of graphs. To obtain a small merged input graph The input features are then passed to the model. The message-passing graph model consists of two encoders, two processors, and one decoder. Each encoder, processor, and decoder is implemented through an MLP consisting of two fully connected (FC) layers (configured as "FC1-ReLU-FC2"). The first FC layer maps the input features to... Hidden space. Besides... , and In addition, the second FC layer is normalized using the LayerNorm operator.

[0076] S4. Feature clustering is achieved by using subgraph splitting operation, which reduces the global cross-scale range, reduces the difficulty of aggregating local features, and alleviates the computational burden of directly processing large-scale simulation data during the training process. Will Figure 4 The graph learning model shown is applied to high-precision stress field prediction. For large-scale graphs, a divide-and-conquer strategy and clustering algorithm are used to process the large-scale stress graphs. = 757,872 = 55,512,400 Divided into Subgraph. The message-passing graph model directly predicts the geometry and stress distribution after fluid-structure interaction deformation from the initial node coordinates, implemented using PyTorch and PyTorch Geometric. Furthermore, the message-passing graph model was trained for 500 epochs on an NVIDIA A6000 RTX GPU using the Adam optimizer, with hyperparameters... After the hyperparameter search, Minimizing the loss L on the training cases within the minimum batch B allows the model to learn from the data to update the graph model.

[0077] Furthermore, to evaluate the quality of the predictions, this study adopts the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) criteria commonly used in computer vision, which are defined as follows:

[0078] in, It represents the maximum value of the actual physical quantity; and These are the mean and variance operators; for and Covariance between; constant and Used to ensure computational stability. The PSNR index is measured in decibels (dB), and a higher value indicates better prediction performance. For example, if the PSNR value is less than 20 dB, the accompanying flow field image is severely distorted, and the image prediction quality is unacceptable. If the PSNR value exceeds 35 dB, the predicted image has reached a high level of accuracy. Furthermore, the SSIM value ranges from 0 to 1; the closer the SSIM value is to 1, the higher the image quality.

[0079] Table 2. Message-passing graph neural network for blades Prediction comparison

[0080] Global in Table 2 Prediction results show that the message passing graph model outperforms POD-GPR in all cases, with higher PSNR and SSIM, indicating that... The accuracy and stability of the predictions are better. Figure 5 The results visually demonstrate the predictions of the fluid-structure interaction and message-passing graph models across four test cases. Field. Statistical analysis, except This also includes diagonal distributions and Gaussian mixture distributions. To better filter the message-passing graphical model's ability to learn stress-deformation features, three components are used. An approximation was made. Finally, Table 2 shows the training cost of the message passing graph model, which can achieve a speedup of 300x when the model is fully trained.

[0081] Table 3. Comparison of training time, inference time, and parameter size between numerical simulation and message passing graph models.

[0082] Finally, the surrogate model is visualized and encapsulated, namely S5, which encapsulates the trained graph model and realizes real-time simulation of the high-dimensional physical field of pump spray under human-computer interaction based on 3D visualization technology and computer graphics, supporting visualization of stress distribution and deformation animation.

[0083] To integrate the new theories, methods, and key technologies of intelligent and agile prediction of pump-jet multiphysics based on graph representation learning developed in this invention, such as... Figure 6 As shown, a pump-jet fluid-structure interaction digital platform will be developed based on Python. Finally, the aforementioned pump-jet multiphysics prediction model based on a message-passing graph model will be completed. This invention addresses the unstructured three-dimensional physics of pump-jet systems in fluid-structure interaction scenarios. Based on different geometric parameters, it verifies the intelligent modeling application of key methods and technologies in this project, evaluating their theoretical accuracy and engineering applicability. Figure 6 The image shows version 1.0 of the pump-jet panoramic fluid-structure interaction digital platform, whose visualization rendering task includes four steps: 1) Import the pump injection unstructured mesh data file using the "File" button in the platform directory; 2) Select the Variable Geometry task in the "Tasks" menu, and configure the graph model in the left control panel; 3) Clicking the "Visual Operation" button allows for interactive color mapping of the physics field cloud map; 4) Based on the graphical model trained in this work, we can quickly predict the multiphysics field of the pump nozzle under varying geometric parameters, and visualize the geometric deformation of the pump nozzle under fluid-structure interaction by adjusting the magnification factor.

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A digital twin method for fluid-structure interaction of pump-jet propulsion based on message-passing graph neural networks, characterized in that, Includes the following steps: S1. Based on the selection of geometric parameters and inverse parameterization modeling of the blade spatial stacking law, an adjustable geometric model of the pump-jet propulsion system is constructed. S2. Under the automated solution framework, uniform sampling or Latin hypercube sampling is used to generate a fluid-structure interaction multiphysics simulation dataset. The fluid-structure interaction multiphysics includes grid node physical quantities and element physical quantities, wherein the element physical quantities include the stress inside the pump impeller element. S3. The fluid-structure interaction multiphysics field attached to the grid nodes and units is characterized as graph structure data, and a deep message passing graph neural network is constructed. The deep message passing graph neural network is used to output the corresponding fluid-structure interaction multiphysics field quantities based on the graph structure data with different geometric shapes input, including the flow field, structural field physical quantities and stress inside the pump impeller unit corresponding to the grid node. S4. Implement large-scale graph data training for deep message-passing graph neural networks through subgraph clustering and block segmentation strategies; S5. Based on 3D visualization and computer graphics technology, an interactive pump-jet propulsion digital twin visualization platform under B / S architecture is constructed to realize parameter adjustment, real-time simulation and dynamic visualization.

2. The method for digital twinning of pump-jet propulsion fluid-structure interaction based on message-passing graph neural networks according to claim 1, characterized in that, In S1, the selection of geometric parameters based on the spatial stacking law of the blade includes: selecting the blade profile shape characteristics and blade spatial stacking parameters as the parameterization index of the propeller blade. The blade profile shape characteristics include chord length, thickness, camber and the position of maximum camber. The blade spatial stacking parameters include pitch, longitudinal tilt and skew. Inverse parametric modeling includes: using B-spline fitting to fit the spatial stacking parameters of the thruster blades, performing parametric fitting via Python to convert the 3D geometric model into a parametric model, and then using AutoGrid5 in NUMECA. TM Generate the corresponding parametric geometric structured mesh.

3. The method for digital twinning of pump-jet propulsion fluid-structure interaction based on message-passing graph neural networks according to claim 1, characterized in that, In S2, under the automated solution framework, uniform sampling or Latin hypercube sampling is used to generate fluid-structure interaction multiphysics simulation datasets, including: The simulation is automated in batches using Python and ANSYS Workbench's CS mode. The fluid-structure interaction results of each sample are stored as an unstructured field dataset in the form of nodes and elements. Determined based on numerical simulation Design variables The geometric parameters are obtained by selecting them through uniform sampling or Latin hypercube sampling. For each sample point, the pump spray mesh under the corresponding geometric parameters is obtained through the inverse parameterization modeling method. Then, the key physical quantities of the sample response value are solved by numerical simulation based on simulation verification. Based on ANSYS workbench and Client-Server mode, Python drives the automated updating of the structured mesh generated by NUMECA, and outputs saved physical field mesh information and calculation results.

4. The method for digital twinning of pump-jet propulsion fluid-structure interaction based on message-passing graph neural networks according to claim 1, characterized in that, In S3, the fluid-structure interaction multiphysics fields attached to mesh nodes and elements are characterized as graph-structured data, including: Define vector It is a collection containing the indices of three-dimensional mesh nodes, a matrix It is an adjacency matrix describing the connections between nodes, and ; Encode the relative displacement of two nodes in the grid space as And convert the relative displacement into mesh edge features. ;in, Indicates relative displacement. express Node coordinates express Node coordinates Indicates spatial dimension, By collecting edge features, the corresponding feature matrix is ​​obtained. in , Indicates the total number of grid nodes. It is the stress embedded inside the pump impeller unit, which serves as the element feature and edge feature matrix. Connections, together constituting the core physical characteristics of a graph structure, define the input graph of a deep message-passing graph neural network as... , where the input matrix The Behavior ,in For related Geometric parameters, To design the variable dimensions, the output graph is defined as follows: The output matrix The Behavior ,in It includes A snapshot of the flow of interest for the physical quantity. For the types of flow field parameters, The structural field parameters are types, including those related to element characteristics. Statistical characteristics of the internal stress of the corresponding pump impeller unit.

5. A method for digital twinning of pump-jet propulsion fluid-structure interaction based on message-passing graph neural networks according to claim 4, characterized in that, In S3, the deep message-passing graph neural network includes a node encoder, an edge encoder, a message-passing processor, an aggregation processor, and a node decoder. Among them, message passing processor Used to update edge features, through the adjacency matrix. To visit via the border Connect to node nodes ,Right now ； Aggregator First, use the operator. For nodes Connected edges Summation, then solving for aggregated features. : pass and The MP aggregation operation will be repeated Next, implement based on In deep structures, message passing strategies gradually expand the neighborhood under consideration to capture features at different scales.

6. The method for digital twinning of pump-jet propulsion fluid-structure interaction based on message-passing graph neural networks according to claim 1, characterized in that, In S4, large-scale graph data training for deep message-passing graph neural networks is achieved through subgraph clustering and block partitioning strategies. This includes using a random multi-clustering strategy to divide the original large-scale graph into several subgraph clusters, and then training in parallel through a cluster-GCN structure.

7. The method for digital twinning of pump-jet propulsion fluid-structure interaction based on message-passing graph neural networks according to claim 1, characterized in that, In S4, large-scale graph data training for deep message-passing graph neural networks is achieved through subgraph clustering and block-based strategies, and also includes: Input image Divided into Each cluster is randomly selected in each batch during model training. Sub-atlas This results in a merged graph. Its corresponding adjacency matrix is: in At this point, the number of edges is The overall time complexity of cluster-GCN is .

8. The method for digital twinning of pump-jet propulsion fluid-structure interaction based on message-passing graph neural network according to claim 1, characterized in that, Based on 3D visualization and computer graphics technologies, an interactive digital twin visualization platform for pump-jet propulsion systems under a B / S architecture is constructed, including: A pre-trained deep message-passing graph neural network is loaded using a server program written in Python. The program receives geometric parameters input by the user and calls the deep message-passing graph neural network in real time to perform multiphysics prediction and generate flow field and structural field data. A dynamic web interface is built based on the Trame framework, integrating parameter input controls and a 3D visualization window, allowing users to adjust geometric parameters online and trigger simulation calculations. Utilize the VTK engine for efficient rendering of unstructured mesh data.

9. A method for digital twinning of pump-jet propulsion fluid-structure interaction based on message-passing graph neural networks according to claim 1, characterized in that, Based on 3D visualization and computer graphics technologies, an interactive digital twin visualization platform for pump-jet propulsion systems under a B / S architecture is constructed, which also includes: Through standardized API interfaces, the interactive pump-jet propulsion digital twin visualization platform can interact with external CFD software and industrial IoT platforms to achieve cross-platform collaborative simulation and multi-source data fusion.

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