A particle tracking velocimetry method based on graph neural networks

Abstract

The application discloses a particle tracking and velocity measurement method based on a graph neural network, realizes matching of particle positions from three-dimensional particle clouds at two time points, and obtains three-dimensional flow field movement velocity, and belongs to the field of flow field visualization measurement. The method comprises particle-velocity field data set formation, graph neural network construction and training, flow field particle image acquisition, particle detection, particle three-dimensional coordinate reconstruction, three-dimensional velocity field estimation, cross-frame particle matching and velocity field post-processing; wherein, the graph neural network adopted by the application obtains network parameters after training, the input of the network parameters is two frames of particle sets at continuous time points, and the output is a velocity field of the first frame of particle sets. Compared with a traditional particle tracking method, the three-dimensional particle tracking and velocity measurement are performed by adopting the application, high-precision velocity fields can be obtained in a scene with high particle density and complex flow, and the neural network adopted by the application has extremely high operation efficiency, and almost no additional calculation time is increased.

Description

Technical Field

[0001] This invention belongs to the field of flow field visualization measurement, and particularly relates to a particle tracking and velocity measurement method based on graph neural networks. Background Technology

[0002] Particle tracking velocimetry (PTV) is a non-contact flow field measurement technique primarily used for the visualization and quantitative measurement of complex fluid motions, playing a crucial role in fluid mechanics theory and experimental research. PTV technology first introduces fluorescent tracer particles into the measured medium to follow the fluid's movement. Simultaneously, laser illumination is used, and a digital camera captures continuous particle images. Then, a cross-frame matching algorithm is employed to obtain the matching relationships between particles and calculate inter-frame displacements, achieving global 3D velocity measurement of the fluid. Establishing the matching relationship between particles in two frames is the key to particle tracking velocimetry.

[0003] Traditional particle tracking (PTV) techniques obtain velocity vectors by associating identical particles with trajectories in consecutive frames. To find the corresponding particles in subsequent frames, a complex iterative process involving manually manipulated parameters is typically employed, sacrificing computational efficiency for high-precision particle motion estimation. Furthermore, classic PTV methods have high requirements for particle density. On one hand, low particle concentration reduces the spatial resolution of PTV motion estimation, leading to inaccuracies in small-scale flow measurements; on the other hand, high particle concentrations cause interference and overlap among a large number of particles, making trajectory matching complex and difficult. Additionally, for complex flow fields with large particle displacements, single-frame tracking often leads to tracking errors. Therefore, classic algorithms introduce additional temporal smoothing across multiple consecutive frames to improve tracking accuracy. However, multi-scale tracking and complex pre- and post-processing increase computational overhead, especially for large-scale particle ensembles, significantly increasing the demands on hardware. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of traditional PTV algorithms, which suffer from low computational accuracy and efficiency over large velocity ranges and high particle concentrations, by providing a particle tracking and velocimetry method based on graph neural networks. This method combines computer vision with PTV technology, significantly improving PTV computational efficiency while ensuring high-precision estimation of small-scale flow structures in complex fluids.

[0005] To achieve the above objectives, this invention provides a particle tracking and velocity measurement method based on graph neural networks, comprising the following steps:

[0006] (1) Generate a PTV dataset, which contains particle coordinates and corresponding velocity field labels. Each data item used for training in the PTV dataset contains two consecutive sets of particle coordinates and corresponding velocity vector fields.

[0007] (2) The graph neural network model is trained using the PTV dataset generated in step (1); the graph neural network model takes the two-frame particle coordinate set as input and outputs the velocity vector field corresponding to the predicted particle coordinate set;

[0008] (3) Use multiple cameras to capture flow field images, identify particles from images at consecutive time points and reconstruct the three-dimensional coordinates of the particles;

[0009] (4) Input the set of particle coordinates at consecutive time moments into the trained graph neural network model to calculate the velocity vector field corresponding to each particle in the first frame of the particle set;

[0010] (5) Apply initial displacement to the particle set in the first frame based on the velocity vector field output by the graph neural network model, and execute the standard PTV cross-frame matching algorithm to obtain the final velocity field through the matching relationship between particles; or calculate the optimal transport matrix through the graph neural network model and establish the particle matching relationship to obtain the final velocity field.

[0011] (6) Post-process the final velocity field to obtain accurate PTV velocity field measurement results.

[0012] Furthermore, in step (1), a first frame particle set P with randomly distributed coordinates is generated within the three-dimensional observation area. The first frame particle set P contains more than two thousand randomly distributed particles in the 3D observation volume, and the observation volume is defined at a random position in the computational fluid dynamics computational domain.

[0013] Furthermore, the particle ensemble is generated by the simulator, and the shape of each particle in space satisfies a three-dimensional Gaussian distribution:

[0014]

[0015] Where x, y, z represent the three-dimensional spatial coordinates in the image, x0, y0, z0 represent the particle center position, I represents the grayscale intensity of a single particle, I0 represents the peak intensity value at the particle center, and d p The diameter of the particle is given.

[0016] Furthermore, step (2) includes the following sub-steps:

[0017] (2.1) Construct a graph neural network model, taking the two-frame particle set (P,Q) as the network input, and the network output is the velocity vector field V corresponding to the first frame particle set P. e ;

[0018] (2.2) Set the loss function for training the graph neural network model to optimize the network parameters, with the following expression:

[0019]

[0020] Among them, V i e Let ||·|| represent the particle motion estimate for the i-th iteration, ||·|| represent the L1 distance, and λ represent the distance between the two particles. i The weights represent the error of the i-th iteration result, where λ i It follows an exponential distribution;

[0021] (2.3) Optimize network parameters through forward computation and backpropagation of error. Train a graph neural network model using the PTV dataset. Use the coordinates of the particle set as the network input and the velocity vector field as the network output label. Use the loss function to calculate the error between the network output and the label. Use the adaptive moment estimation algorithm to optimize the network parameters to obtain a graph neural network model for particle tracking and velocity measurement.

[0022] Further, step (2.1) includes: extracting a static geometry G from the particle ensemble. s With dynamic feature map G d Generate particle depth feature descriptor F G The optimal transmission scheme T between two particle sets is calculated based on this depth feature. Adaptive point-voxel retrieval is used to characterize the correlation between particles. Furthermore, the spatial distribution context features of the particles are extracted and input into the gated recurrent unit for iterative updating. Here, given the initial displacement field V0 e The update unit outputs the displacement field change ΔV in each iteration. e The final output is the velocity vector field V corresponding to each particle in the particle set P. e .

[0023] Furthermore, the static geometry G s Vertex V er G consists of the entire set of particles P or Q. s The edge is formed by passing each particle p i It is formed by connecting its k nearest neighbor particles; each edge connects particle p. i It forms a local geometry with its k nearest neighbor particles, and further constructs p i Vertex features Where, p ik Represents particle p i The k-th nearest neighbor particle, p ik -p i r represents the difference in particle coordinates in three-dimensional space. ik θik and These represent the radial distance, azimuth angle, and polar angle of adjacent particles in the spherical coordinate system, respectively.

[0024] Furthermore, in step (6), the post-processing includes smoothing and noise removal.

[0025] The beneficial effects of this invention are: this invention uses graph neural networks for particle tracking and velocities, which improves computational efficiency while ensuring high accuracy; it uses PTV datasets to train the neural network, which can accurately extract the particle velocity field from two sets of particles; compared with traditional particle matching methods, this invention can effectively estimate small-scale vortex structures and improve the estimation accuracy of PTV technology for high particle density and large displacement scenes. Attached Figure Description

[0026] Figure 1 This is a flowchart of the implementation steps of the present invention;

[0027] Figure 2 This is a schematic diagram of the data generation process described in the embodiment; wherein Figure 2 (a) in the text represents the particle set P of the first frame. Figure 2 In the diagram, (b) represents the known velocity vector field V. Figure 2 (c) in the example uses V to move the particle set P to generate the second frame particle set Q;

[0028] Figure 3 This is a schematic diagram of the graph neural network structure described in this example;

[0029] Figure 4 This is a schematic diagram of the particle tracking and velocimetry device provided by the present invention;

[0030] Figure 5 This is a schematic diagram of the reconstruction of three-dimensional spatial particle coordinates as described in this example.

[0031] Figure 6 This is a graph showing the input and output results of the graph neural network described in the embodiment.

[0032] Symbol explanation: 1-Water tank, 2-Tracer particles, 3-Dual pulse laser, 4-Beam expander, 5-CCD camera, 6-Control system. Detailed Implementation

[0033] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0034] This invention provides a particle tracking and velocity measurement method based on graph neural networks. This method uses supervised learning graph neural networks to extract and analyze the velocity field from the coordinates of three-dimensional fluid particles. Figure 1 The following is a flowchart illustrating the implementation of the method of the present invention, which includes the following steps:

[0035] Step 1: Generate the PTV dataset;

[0036] The PTV training dataset refers to a large number of artificially synthesized particle coordinates and corresponding velocity field labels in three-dimensional space, used for training graph neural network models. Each data item used for training in the dataset contains two consecutive frames of particle coordinates (P, Q) and a real velocity vector field V.

[0037] In this embodiment of the invention, the steps for generating data items are as follows: Figure 2 (a) Figure 2 (b) and Figure 2 As shown in (c), a first frame particle set P with randomly distributed coordinates is first generated within the 3D observation region. The first frame particle set P contains more than two thousand randomly distributed particles in the 3D observation volume, which is defined at random locations within the computational fluid dynamics (CFD) computational domain. The next frame position of the first frame particle set P, i.e., the second frame particle set Q, is obtained using the integral trajectory at specified time intervals. Subsequently, the corresponding true velocity vector field (displacement) V = QP is obtained.

[0038] In this embodiment of the invention, the particle set is generated by a simulator, and the shape of each particle in space satisfies a three-dimensional Gaussian distribution:

[0039]

[0040] Where x, y, z represent the three-dimensional spatial coordinates in the image, x0, y0, z0 represent the particle center position, I represents the grayscale intensity of a single particle, I0 represents the peak intensity value at the particle center, and d p The diameter of the particle is given.

[0041] In this embodiment of the invention, the size of the three-dimensional observation area and the integration time interval can be defined according to requirements. For example, the size of the three-dimensional observation area can be defined as a cuboid region between the coordinate origin [0,0,0] and [π,2,π]; the integration time interval can be defined between [0.03-1.4]. Using a small time interval can obtain a small displacement scene particle set, while a large time interval results in a large displacement scene sample.

[0042] To ensure dataset diversity, different data samples have different parameters, including particle diameter (1-4 voxels), displacement ratio (0.35-6.58), particle peak gray level (200-255), particle localization error (Δx∈[0,0.25] voxels), and noise level n∈[0,1]. The particle localization error Δx reflects the accuracy of particle coordinate reconstruction and is achieved by adding Gaussian noise to the particle's three-dimensional coordinates. The noise level reflects measurement noise, occlusion phenomena, and particles leaving (or entering) the observation area. Specifically, the order of particles in the particle set Q is first shuffled, and then n% of the particles in Q are randomly replaced with newly generated randomly distributed particles.

[0043] The velocity vector field V can represent various fluid motion scenarios, including: three-dimensional uniform flow fields, Beltrami flow fields, incompressible isotropic turbulence, magnetohydrodynamic turbulence, turbulent channel flow, and transitional boundary layer flow. This example... Figure 2 The velocity field shown in (b) is a uniform flow field.

[0044] In this embodiment of the invention, a generated PTV dataset is obtained; the PTV dataset contains 16,000 particle pairs (P,Q) and the corresponding velocity vector field V.

[0045] Step 2: Build a graph neural network and train the network;

[0046] The network parameters of the graph neural network model are trained using the PTV dataset synthesized in step one. This network can be represented as V. e =F(P,Q), where P and Q represent the particle sets of the two input frames, and V e This represents the network output, i.e., the velocity vector field corresponding to the predicted particle set P, and F represents the mapping function of the graph neural network. Specifically, building the network structure and training the network parameters using the PTV dataset includes:

[0047] (2.1) Construct a network structure model, taking the two-frame particle set (P,Q) as the network input, and the network output is the velocity vector field V corresponding to the first frame particle set P. e .

[0048] Network models such as Figure 3 As shown. This network extracts the static geometry G from the particle ensemble. s With dynamic feature map G d Further, a particle depth feature descriptor F is generated. G The optimal transmission scheme T between two particle sets is calculated using this depth feature. Adaptive point-voxel retrieval is used to characterize the correlation between particles. Furthermore, the spatial distribution context features of the particles are extracted and input into the gated recurrent unit for iterative updating. Given an initial displacement field... The update unit outputs the displacement field change ΔV in each iteration. e The final output is the velocity vector field V corresponding to each particle in the particle set P. e .

[0049] In this embodiment of the invention, the static geometric diagram G s Vertex V er G consists of the entire set of particles P (or Q). s The edges are formed by p of each particle (i.e., vertex). i Each edge connects to its k nearest neighbor particles, where the nearest neighbor search is performed using a distance metric in three-dimensional Euclidean space. k can be defined according to requirements; using a larger k value takes into account more neighboring particle information. In this embodiment, k = 32. Each edge connects particle p... i It forms a local geometry with its k nearest neighbor particles, and further constructs p i Vertex features Where, p ik Represents particle p i The k-th nearest neighbor particle, p ik -p i r represents the difference in particle coordinates in three-dimensional space. ik θ ik and These represent the radial distance, azimuth angle, and polar angle of adjacent particles in the spherical coordinate system, respectively. This spherical coordinate representation further preserves the rotation-invariant correspondences in geometric space. The static geometric diagram G of the particle ensemble. s It only needs to be computed once before network training, and deep features are generated after a series of graph convolution and pooling operations.

[0050] Given a set of particles P and its static geometry G s A graph convolutional neural network is used to encode the local geometric features of each particle to generate a unique feature descriptor for each particle. For the β-th static graph convolution, it encodes the graph vertices p... i Features Mapping to new features

[0051]

[0052] in, Represents vertex p in a static geometric graph i The set of the k nearest neighbors of φ β (·) is the β-th static graph convolutional layer, which consists of multiple perceptrons. In this embodiment, β = {1,2,3}; max represents the max pooling operation to aggregate the features of k neighboring particles; Initialize p in the first graph convolutional layeri Three-dimensional spatial coordinates f i .

[0053] To further enrich the feature representation of local geometric information of particles, a dynamic graph feature extractor was designed. Specifically, the dynamic graph G... d =(V er E d ), where G d With G s Sharing the same vertex V er And G d The edge E d Then by each particle (vertices) p i It is formed by connecting with its k nearest neighbor particles in the characteristic space. Vertex V er With edge E d It also forms a local structure in the feature space, and then p on the dynamic graph of the γth layer. i Vertex features The update process is as follows:

[0054]

[0055] in p represents each particle in the characteristic space i The indices of the k nearest neighbor particles; This represents the γth dynamic graph convolutional layer, which is implemented using a multilayer perceptron. In this embodiment, γ = {1,2}. Initialize to Static graphs have a receptive field limited to a local domain and cannot capture long-distance relationships between particles (graph vertices). Dynamic graphs, on the other hand, extend the receptive field to the entire set of particles through operations on a high-dimensional feature space, and dynamically construct the graph through network learning.

[0056] Then, for the two graph structures from different layers and The data is concatenated along the channel dimension and a series of multilayer perceptron structures with skip connections are used to generate the final deep particle feature F. G :

[0057]

[0058] Where ψ(·) represents a multilayer perceptron; This represents the splicing operation of particle features from different graph structures and layers. The final deep particle feature F G This will be used to specify the optimal subsequent transport scheme to infer particle correspondences through the similarity between features. Additionally, another feature encoder is used to extract contextual features F of the spatial distribution of particles in P. C .

[0059] In this embodiment of the invention, the optimal transmission scheme refers to finding the optimal transmission scheme for converting the first frame particle set P into the second frame particle set Q (i.e., the target particle set), which has the minimum transmission cost. Specifically, each particle p in the two particle sets... i (q j The quality setting is as follows: Optimal transfer scheme between two particle sets The definition is as follows:

[0060]

[0061]

[0062] Where n1 and n2 represent the number of particles in the two particle sets, respectively; C ij It is particle p i ∈P is transmitted to particle q j The cost required to ∈Q. U ij Indicates from particle p i Transmitted to q j The specified quality. Furthermore, the equality constraints define... and This constraint states that each particle p from the first frame particle set... i The mass is fully delivered to the target distribution, and each particle q in the target distribution... j The volume of the transported material is completely filled. Transmission cost C ij Defined as each particle p in the two-frame particle set i and q j Deep particle characteristics F G (p i ) and F G (q j Negative cosine similarity of )

[0063]

[0064] Where ||·||2 represents the l2 norm. If p i With q j If the transmission cost between them is low, the optimal transmission solver will tend to transfer more p... i The mass moves to q j The optimal transport scheme characterizes each particle p in the first frame. i Each particle q in the second frame j The correspondence between them. The value at (i,j) in the optimal transport scheme matrix T represents the value from p. i Transmit to q jThe greater the mass of the transmitted particles, the stronger the correspondence between the two particles. The optimal transmission scheme matrix T is constructed only once and stored for subsequent retrieval processes.

[0065] In this embodiment of the invention, adaptive point-voxel retrieval is a strategy that can effectively retrieve the correlation between near-range and far-range particles in the optimal transport scheme T, that is, retrieve the transport scheme T corresponding to the neighboring particles. t By fusing the retrieved point-based transmission scheme T p (·) and voxel-based transmission scheme T v (·) is used to provide the correspondence between long-range and short-range particles for subsequent motion iteration updates:

[0066] T t =T p (P t ',Q)+T v (P t ',Q)

[0067] Among them, P t =P+V t e This indicates that the particle set P of the first frame is predicted to have a displacement V during the t-th iteration. t e Moved to the new location. T p (·) Through dynamic k t The nearest neighbor search strategy is used for retrieval, and the number of neighboring particles retrieved in each iteration gradually decreases as the process progresses, and k t =k0-ηt, where k0 is k t The initial values ​​are given by η, which is a constant value; for example, k0 = 32 and η = 2. To address the large-scale motion implicit in the long-distance relationships of the optimal transport scheme, an adaptively variable multi-scale cuboid voxel structure is constructed. This cuboid divides the geometric space containing the particles into multi-scale pyramid voxels to generate the voxel-based optimal transport scheme T. v Specifically, each constructed cuboid is based on P. t Centered on each particle, and collecting neighboring particles enclosed in Q, the voxel cuboid is composed of d 3 It consists of identical sub-cubic prisms, with a length of width and height The vector is adaptively defined based on the motion update in the most recent iteration:

[0068]

[0069] Where S(|Δf) l |) and S(|Δf l-1|) represent P respectively t The normalized length of the current and previous motion updates of all particles in the network is used to prompt the network to search for corresponding transmission schemes over a wider range when there are significant changes in the motion updates during the iteration process; cos<Δf l ,Δf l-1 The cosine similarity of motion updates in two iterations was calculated. When the two motion updates are consistent, a higher cosine similarity value will further strengthen the network's search for corresponding transmission schemes over larger distances in that direction; conversely, a lower value will lead to a smaller search range. Furthermore, and These are the unit orthogonal basis vectors on the three components used to guide the search direction. r is the basic size parameter of the adaptively variable cuboid voxel element, r = 2. s-1 d m α, where d m This represents each particle in the input particle set and its k. d The mean of the average distances between the nearest neighbor particles is used to obtain local particle concentration information. α is a learnable scale parameter during network training and optimization. s is the number of pyramid layers. In this embodiment, s = {1, 2, 3, 4}.

[0070] (2.2) Set the loss function for network training.

[0071] After designing the network structure, a network objective function needs to be set to optimize the network parameters. This can be specified as the particle motion estimation sequence output during network iteration. With the label velocity field V gt The error is calculated using the following formula:

[0072]

[0073] Among them, V i e Let ||·|| represent the particle motion estimate for the i-th iteration, ||·|| represent the L1 distance, and λ represent the distance between the two particles. i The weights represent the error of the i-th iteration result, where λ i Follows an exponential distribution, λ i =μ iter-i In this embodiment, μ is set to 0.8 and iter is set to 10.

[0074] (2.3) Optimize network parameters through forward computation and error backpropagation.

[0075] After setting the network structure and objective function, optimization strategies are needed to train the network parameters. The graph neural network is trained using the artificially synthesized PTV dataset from step one. The coordinates of the particle set (P,Q) are used as the network input, and the real displacement field V is used as the network output label. The loss function from step (2.2) is used to calculate the error between the network output and the label, and the Adaptive Moment Estimation (Adam) algorithm is employed to optimize the network parameters, thus obtaining a graph neural network model that can be used for particle tracking and velocity measurement.

[0076] Step 3: Input the particle coordinates into the trained network model to calculate the particle velocity field;

[0077] For the graph neural network model trained in step two, when inputting the three-dimensional coordinates of the particles obtained from the real experiment in practical applications, the set of particle coordinates (P,Q) at consecutive time moments can be obtained, and the displacement field corresponding to the first frame of particle set can be predicted.

[0078] The actual experimental process refers to capturing flow field images, identifying particles, and reconstructing particle coordinates in three-dimensional space;

[0079] The aforementioned capturing of the flow field images refers to using multiple cameras to record images of tracer particles within the measurement area of ​​the flow field from different angles. For example, to measure the three-dimensional velocity field of a complex flow in water tank 1, the specific implementation of the hardware measurement system proposed in this invention is as follows: Figure 4 As shown, tracer particles 2 are uniformly mixed into water tank 1. The test area is illuminated using a dual-pulse laser 3 and a beam expander 4. Four CCD cameras 5 are arranged in a straight line or cross shape to take cross-frame photos of the exposed tracer particles 2 in the same area from different angles. The synchronous operation of the cameras and lasers is controlled by a synchronization controller 6. Four camera images from different perspectives are obtained at each moment, and are transmitted to a computer via a data cable for storage.

[0080] The process of identifying particles and reconstructing particle coordinates in three-dimensional space refers to obtaining the pixel coordinates of tracer particles in each viewpoint camera image using the PTV particle recognition algorithm, and then using an iterative particle reconstruction method to obtain the particle coordinates in three-dimensional space. Figure 5 As shown.

[0081] Step 4: Input the particle coordinates into the trained graph neural network model to calculate the velocity vector field corresponding to the particle;

[0082] The step involves using the particle coordinate set (P, Q) obtained in step three as input, and then using the graph neural network model F(·) trained in step two to calculate the velocity vector field V corresponding to each particle in the first frame particle set. This step can be represented as follows: Figure 6In this embodiment, the wake velocity field of the flow around the cylinder is calculated. This flow is an incompressible fluid with a Reynolds number of 3900 and 2000 particles distributed in the flow field. The results of this embodiment show that the proposed method effectively resolves the observed turbulent structure in the flow field. This embodiment of the invention can resolve flow fields not limited to 2000 particles. When the number of particles in the flow field exceeds 3000, the flow field can be divided into multiple small regions before being input into the network model to ensure that the number of particles in each region is within 2000, thereby achieving better prediction results. This is because the neural network model only used 2048 particles during training, therefore the network's optimal performance is also achieved under the condition of 2048 particles.

[0083] Step 5: Apply an initial displacement to the particle set in the first frame and execute the standard PTV cross-frame matching algorithm;

[0084] After obtaining the predicted displacement of the particle set in the first frame through step four, the velocity vector field V output by the graph neural network model is... e As the initial displacement of the first frame particle set P, it is applied to the first frame particle coordinates to obtain the new position (P+V). e Then, for the particle set (P+V) after the motion... e Q) The standard PTV cross-frame matching algorithm is executed to obtain the accurate flow field velocity V (i.e. the final velocity field) by establishing the matching relationship between particles in the first frame particle set P and the second frame particle set Q.

[0085] Alternatively, the matching relationship between particle set P and particle set Q can be directly established using the graph neural network model trained in step two. The 3D coordinates of the particles obtained in step three are input into the graph neural network trained in step two. The matching relationship between particles is established based on the optimal transport matrix T calculated in the middle of the network. The velocity field vector is obtained through the coordinate difference of the matched particles, and outlier removal is used to correct the displacement field. For unmatched particles, the following steps are iterated: the velocity at the coordinates of the unmatched particles is obtained by interpolation based on the velocity field vectors of the matched particles; the particle set P is moved using the velocity field vector; the graph neural network model trained in step two is input; the optimal transport matrix is ​​calculated to establish the matching relationship between particles; the velocity field is obtained; and outlier removal is performed.

[0086] The matching relationship between particles obtained by the intermediate calculation of the network based on the optimal transport matrix T refers to selecting particles in particle set Q that match particle set P by using the maximum row value of the optimal transport matrix, and selecting particles in particle set P that match particle set Q by using the maximum column value of the optimal transport matrix. Based on the uniqueness of the matching, the matching is considered correct when both particles match each other.

[0087] Step 6: Post-process the velocity field to obtain the final result.

[0088] The post-processing refers to the post-processing of the final velocity field V obtained in step five to ultimately achieve PTV velocity field measurement. In this embodiment, median filtering is used to process the velocity field, and the filter kernel size is 3×3.

Claims

1. A particle tracking and velocity measurement method based on graph neural networks, characterized in that, Includes the following steps: (1) Generate a PTV dataset, which contains particle coordinates and corresponding velocity field labels. Each data item used for training in the PTV dataset contains two consecutive sets of particle coordinates and corresponding velocity vector fields. (2) The graph neural network model is trained using the PTV dataset generated in step (1), so that the graph neural network model generates the optimal transport matrix between the two sets of particle coordinates during the forward computation process after receiving two consecutive sets of particle coordinates. (3) Use multiple cameras to capture flow field images, identify particles from images at consecutive time points and reconstruct the three-dimensional coordinates of the particles to obtain the first frame of particle set. P ={ p i } and the second frame particle set Q ={ q j }; (4) The first frame particle set P Second frame particle set Q Input the trained graph neural network model, and directly extract the optimal transport matrix calculated by the intermediate layers of the network during the forward computation of the graph neural network model. T ; (5) Based on the optimal transport matrix T Establishing particle matching relationships specifically includes: For the first frame of particle set P Particles in p i The optimal transport matrix T is passed through the first... i The maximum value in the row determines the candidate matching particles in the particle set Q of the second frame. q j ; For the second frame of particle set Q Particles in q j Through the optimal transport matrix T The j The maximum value in the column determines the particle set in the first frame. P Candidate matching particles p i '; If and only if i '= i At that time, the particle was identified p i With particles q j Both parties are matched with each other, and a particle matching relationship is established between them; otherwise, a particle matching relationship is not established between them. (6) Calculate the velocity vector based on the three-dimensional coordinate difference of the established matching particle pairs to obtain the PTV velocity field; (7) For particles that have not established a matching relationship, the velocity at the coordinates of the unmatched particles is obtained by interpolating the velocity vector of the particles that have established a matching relationship. The first frame of particles is moved using the velocity vector obtained by interpolation. The first frame of particles and the second frame of particles after the movement are input into the trained graph neural network model again. Steps (4) to (6) are repeated to iteratively establish the particle matching relationship of the unmatched particles. (8) Post-process the PTV velocity field to obtain the PTV velocity field measurement results.

2. The particle tracking and velocity measurement method based on graph neural networks according to claim 1, characterized in that, In step (1), a first frame set of particles with randomly distributed coordinates is generated within the three-dimensional observation area. First frame particle set It contains more than two thousand randomly distributed particles in a 3D observation volume, which is defined at random locations in the computational fluid dynamics computational domain.

3. The particle tracking and velocity measurement method based on graph neural networks according to claim 1, characterized in that, In step (1), the particle set is generated by the simulator, and the shape of each particle in space satisfies a three-dimensional Gaussian distribution: ， in, Represents the three-dimensional spatial coordinates in the image. Represents the position of the particle's center. Represents the gray intensity of a single particle. The peak intensity value representing the particle center, The diameter of the particle is given.

4. The particle tracking and velocity measurement method based on graph neural networks according to claim 1, characterized in that, Step (2) includes the following sub-steps: (2.1) Construct a graph neural network model to combine the particle sets of the two frames. As network input; (2.2) Set the loss function for training the graph neural network model, and use the velocity field label as supervision information to optimize the network parameters; (2.3) By optimizing the network parameters through forward computation and backpropagation of error, a graph neural network model is obtained to generate the optimal transport matrix between two sets of particles during the forward computation process.

5. The particle tracking and velocity measurement method based on graph neural networks according to claim 1, characterized in that, The graph neural network model extracts static geometric graphs and dynamic feature graphs from the particle set, generates particle depth feature descriptors, and calculates the optimal transport matrix between two particle sets using the particle depth feature descriptors; in step (4), the optimal transport matrix is ​​directly extracted from the intermediate layer of the graph neural network model and used for the calculation based on the optimal transport matrix. T Steps for establishing particle matching relationships.

6. The particle tracking and velocity measurement method based on graph neural networks according to claim 5, characterized in that, The vertices of the static geometry are composed of a given set of particles, and the edges of the static geometry are formed by connecting each particle to its corresponding particle. k It is formed by connecting the nearest neighbor particles; each edge connects the particle to its nearest neighbor particles. k The local geometry is composed of neighboring particles, and vertex features are constructed. The vertex features include the three-dimensional coordinate difference between neighboring particles and the radial distance, azimuth angle and polar angle of neighboring particles in the spherical coordinate system.

7. The particle tracking and velocity measurement method based on graph neural networks according to claim 1, characterized in that, The post-processing includes outlier removal, smoothing, and noise removal of the PTV velocity field.

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