A self-supervised three-dimensional particle tracking velocimetry method

Abstract

This invention relates to a self-supervised 3D particle tracking and velocity measurement method, comprising the following steps: S1, acquiring a continuous temporal sequence of 3D source particle sets and 3D target particle sets, and performing feature encoding to obtain the feature matrix of the corresponding particle sets; S2, inputting the feature matrices of the source particle sets and target particle sets into a DFCT, and outputting the aligned cross-frame features; S3, constructing a transmission cost matrix between particles, establishing a dense soft correspondence between particles in two frames, and outputting the initial flow field estimation result and matching confidence; S4, constructing a composite self-supervised loss function, and iteratively optimizing the model parameters by minimizing the composite self-supervised loss function; S5, refining the initial flow field estimation result, and outputting the final 3D fluid velocity field. The beneficial effects of this invention are: solving the problems of algorithm dependence on large-scale high-quality labeled data, low efficiency in extracting semantic features from complex flow field point clouds, and matching ambiguity in high-displacement, high-density scenarios.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional particle tracking and velocimetry technology, and specifically to a self-supervised three-dimensional particle tracking and velocimetry method. Background Technology

[0002] Understanding and quantifying fluid motion (especially turbulence) is a core challenge in fluid mechanics and industrial engineering. Three-dimensional particle tracking velocimetry (3DPTV), as a non-invasive measurement technique with high spatial resolution, reconstructs the three-dimensional instantaneous velocity field by tracking and tracing particle trajectories, offering the advantage of a fine Lagrangian description.

[0003] In existing technologies, traditional PTV algorithms, such as relaxation labeling or iterative prediction and reconstruction algorithms, mainly rely on geometric matching or statistical correlation. They face huge computational overhead when dealing with high-concentration, high-shear flow fields. Furthermore, their over-reliance on artificial parameters results in poor robustness to image noise and particle overlap. Moreover, supervised learning-based methods rely heavily on artificially synthesized datasets with ground truth labels for training. Obtaining motion labels for real flow fields in actual physical experiments is extremely difficult, leading to a significant decrease in the model's generalization ability when facing real scientific or industrial scenarios. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this application proposes a self-supervised 3D particle tracking and velocimetry method, which can solve the problems of existing algorithms heavily relying on large-scale high-quality label data, low efficiency in extracting semantic features from complex flow field point clouds, and matching ambiguity in high-displacement, high-density scenarios.

[0005] The following is the technical solution of the present invention: a self-supervised three-dimensional particle tracking and velocity measurement method, comprising the following steps: S1. Obtain the three-dimensional source particle set and the three-dimensional target particle set in continuous time sequence. Encode the features of the source particle set and the target particle set respectively through the self-learning Geometric Dynamic Graph Convolutional (SG-DGCNN) network to obtain the feature matrix of the corresponding particle set. S2. Input the feature matrices of the source particle set and the target particle set into the dual-filter cross-transformer (DFCT) network. Perform temporal alignment and semantic enhancement of the particle features of the two frames through the dual-filter cross-attention (DFCA) mechanism, and output the aligned cross-frame features. S3. Based on the cross-frame features after alignment, the transmission cost matrix between particles is constructed through the optimal transmission theory. The global transmission plan is solved by the Sinkhorn algorithm to establish a dense soft correspondence between particles in two frames and output the initial flow field estimation results and matching confidence. S4. Construct a composite self-supervised loss function that integrates fluid physics constraints, and iteratively optimize the model parameters by minimizing the composite self-supervised loss function; S5. With the pre-trained model parameters frozen, the initial flow field estimation results are refined by iteratively optimizing the learnable residual flow tensor, and the final three-dimensional fluid velocity field is output.

[0006] As a preferred embodiment of the present invention, S1 includes the following steps: S101. For each central particle in the particle set and its k nearest neighbor particles, construct a static geometric graph in the three-dimensional coordinate space, and generate a 6-dimensional composite geometric feature vector for each edge formed by the central particle and the neighbor particles. The 6-dimensional composite geometric feature vector integrates the 3D relative coordinates from the central particle to the neighbor particles, the Euclidean distance between the central particle and the neighbor particles, and the polar angle and azimuth angle spherical coordinate features observed from the central particle to the neighbor particles. S102. A parallel dual-branch architecture of geometric feature path and dynamic graph feature path is adopted. The geometric feature path extracts the spatial geometric attributes of particles through stacked geometric perception graph convolutional modules, while the dynamic graph feature path dynamically updates the k-NN graph in the feature space through serial dynamic edge convolutional layers to capture the semantic topological relationships of particles. S103. The output features of different depths of the geometric feature path and the output features of the dynamic graph feature path are concatenated by channel dimension, and then compressed and refined by a multilayer perceptron to generate a 128-dimensional feature vector corresponding to each particle, forming a feature matrix.

[0007] As a preferred embodiment of the present invention, in S102, a self-learning hybrid pooling strategy is used to aggregate neighborhood features, including: For the composite edge features generated by the geometry-aware graph convolutional module, a high-level feature representation is obtained by processing them through a 1×1 convolutional layer. The attention weights of the neighborhood dimension are calculated by using two layers of multilayer perceptron and the Softmax function. The attention weights are then multiplied element-wise with the high-level feature representation to obtain the optimized graph features. Four pooling methods—max pooling, mean pooling, sum pooling, and adaptive pooling—are used in parallel to extract neighborhood-dimensional features from the optimized graph features. The features output by the four pooling methods are then concatenated along the channel dimension and compressed and refined by a feature fusion network to complete neighborhood feature aggregation.

[0008] In a preferred embodiment of the present invention, in S2, the DFCT is composed of multiple cascaded DFCA layers stacked with a feedforward neural network (FFN), employing a residual connection architecture; the DFCA includes the following steps: S201. For each particle in the query frame, first narrow the matching search range by spatial k-NN filtering, and then dynamically update the matching candidate set by feature similarity filtering. S202. Perform layer normalization on the feature matrices of the input source particle set and target particle set, and input the particle position information into the DFCA layer. The output of the double-layer screening and cross-layer is weighted by learnable scalar weights and then superimposed on the original input features through residual connections to generate intermediate features. S203. After performing layer normalization on the intermediate features, input them into FFN. The output of FFN is weighted by learnable scalar weights and then superimposed onto the intermediate features through residual connections, outputting aligned cross-frame features.

[0009] As a preferred embodiment of the present invention, S3 includes the following steps: S301. Based on the aligned cross-frame features, calculate the cosine similarity of features between the source particle and the target particle, define the transmission cost of optimal transmission with cosine similarity, construct the transmission cost matrix, and use the Sinkhorn algorithm to optimize the transmission plan between the two-frame particle sets through entropy regularization and quality regularization. S302. Calculate the soft correspondence weight of each source particle relative to the target particle based on the transmission plan, and calculate the predicted new position of the source particle by weighted average of the target particle positions. S303. Based on the difference between the predicted new position and the original position of the source particle, calculate the initial flow field displacement vector, and at the same time calculate the confidence score of each pair of particles.

[0010] As a preferred embodiment of the present invention, in S4, the total loss function of the composite self-supervised loss function is the sum of the reconstruction loss, the weighted flow field smoothing loss, and the weighted mass conservation loss.

[0011] As a preferred embodiment of the present invention, the reconstruction loss is obtained by calculating the one-way chamfer distance between the reconstructed point cloud after the predicted flow field transformation and the target point cloud, combined with matching confidence weighting, and a regularization term is introduced. The flow field smoothing loss is calculated by constructing a spatial k-NN graph and averaging the flow field vector of each particle with the flow field vectors of its neighboring particles. The distance is obtained and used to constrain the local spatial smoothness of the flow field; The mass conservation loss is calculated by interpolating the point cloud flow field to a three-dimensional regular grid through inverse distance weighting, and then calculating the divergence of the grid flow field. The average of the absolute values ​​of the divergence of all grid points is used to constrain the physical law of mass conservation of incompressible fluids.

[0012] As a preferred embodiment of the present invention, in S4, the model training adopts a step-by-step training strategy, including: In the first stage, SG-DGCNN is trained independently. The original three-dimensional particle coordinates are used as input, and the feature extractor is pre-trained by minimizing the composite self-supervised loss function until convergence. In the second stage, the weights of the pre-trained SG-DGCNN are frozen, and DFCT is trained. The cross-frame feature alignment capability is optimized by minimizing the composite self-supervised loss function, thus completing the training of the overall model.

[0013] As a preferred embodiment of the present invention, S5 includes the following steps: S501. For each test instance, initialize a learnable residual flow tensor with all zeros, and construct a refined flow field by combining the initial flow field output by the pre-trained model. S502. The source particle set is transformed using a refined flow field to generate a reconstructed point cloud. S503. Using reconstruction loss as the objective function, backpropagation is used to iteratively update only the residual flow tensor until convergence. S504: Based on the optimized refined flow field, output the final three-dimensional fluid velocity field.

[0014] As a preferred embodiment of the present invention, it further includes: S6. Perform flow field quantification analysis based on three-dimensional fluid velocity field to determine the equipment structural design scheme.

[0015] The beneficial effects of this invention are: 1. This invention proposes a self-learning pooling geometric dynamic graph convolutional network, which improves the representation ability of unstructured point cloud features. When constructing the graph structure, it not only utilizes three-dimensional rectangular coordinates, but also introduces spherical coordinate features such as Euclidean distance, polar angle, and azimuth angle, which significantly enhances the model's perception of the local spatial layout of particles. In addition, this invention abandons the traditional single pooling method and designs a parallel structure that integrates max pooling, mean pooling, sum pooling, and adaptive pooling. Combined with the attention mechanism, it dynamically adjusts the neighborhood contribution, which can capture the peak, trend, and collective behavior features of fluid motion in a comprehensive manner under sparse environment. 2. In this invention, a DFCT (Digital Directional Computational Transformation) method is designed to solve the matching ambiguity problem in large displacement and high-concentration flow fields. First, the search range is narrowed down using spatial K-NN (Kinetic Neural Network), and then high-quality matching candidates are screened using feature similarity, reducing computational complexity from... Reduce to While ensuring accuracy, it greatly improves processing speed. At the same time, through a multi-layer cross-attention mechanism, the model can learn fine cross-frame temporal correlations and achieve accurate alignment of point cloud features between two frames. 3. In this invention, the reliance on high-quality truth labels is eliminated. The scientific nature of the results is ensured by integrating prior knowledge of fluid mechanics. This invention uses the Sinkhorn algorithm to solve the global transmission plan and establishes dense soft correlations between particles in two frames, providing a reliable mapping basis for unsupervised learning. In addition, by calculating the divergence loss to apply physical constraints of incompressible fluids, it ensures that the predicted flow field is not only geometrically consistent but also physically reasonable. 4. In this invention, a test-time optimization module is introduced during the inference stage, which further enhances the performance of the model in practical applications. The test-time optimization module runs independently for each test instance. By optimizing a learnable residual flow while freezing the model parameters, it effectively eliminates the difference in neighborhood distribution between the training set and the test set, and can correct the inherent reconstruction error in the optimal transmission process. This allows the model to obtain extremely high-fidelity flow field reconstruction results even when data is scarce (e.g., only 1% of training data). 5. In this invention, performance surpasses existing supervised learning methods on extremely small datasets. Its robustness to noise and ability to handle high-density particle fields provide a new, efficient, and low-cost solution for fluid measurement in complex industrial environments and scientific research scenarios. Attached Figure Description

[0016] Figure 1 This is a complete flowchart of the model of the present invention; Figure 2 This is a diagram showing the data flow and model structure of the self-learning graph neural network of the present invention. Figure 3 This is a diagram illustrating the dual-layer screening cross-attention mechanism of the present invention; Figure 4 This invention is compared with other state-of-the-art models in a flow experiment around a cylinder; Figure 5 This is a diagram illustrating the steps of the method of the present invention. Detailed Implementation

[0017] To make the technical problems solved by the present invention, the technical solutions adopted, and the technical effects achieved clearer, the technical solutions of the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Example

[0018] This embodiment provides a self-supervised three-dimensional particle tracking and velocimetry method that quantifies the flow field by analyzing the displacement of suspended tracer particles in continuous time-series point cloud data. The tracer particles can closely follow the movement of the fluid medium.

[0019] In this embodiment, the core task involves processing consecutive two-frame unstructured three-dimensional source particle sets. and target particle set By calculating and estimating the fluid motion vector between two frames This allows for the capture of fluid dynamics characteristics in turbulent environments, where... and These represent the number of particles in the corresponding frame.

[0020] like Figure 1 As shown, the overall processing flow of this embodiment consists of feature encoding, cross-frame alignment, and flow field refinement concatenation stages. First, the original input point cloud pairs... Parallel inputs are fed into a weight-sharing feature extraction network. Using improved SG-DGCNN and DFCT, low-dimensional coordinate data is encoded into high-dimensional feature embeddings rich in local geometric semantic information and cross-frame temporal correlations. Subsequently, the optimal transport module solves the global transport plan based on the calculated feature cost matrix and outputs the initial flow field estimation results through soft correspondences between particles. During model training, network parameters are optimized by minimizing a composite self-supervised loss function consisting of geometric reconstruction loss, flow field smoothness loss, and mass conservation constraints. During inference, this embodiment further introduces a test-time optimization module. With the backbone network parameters frozen, this module iteratively optimizes a learnable residual flow to eliminate domain differences between training and test data, ultimately outputting a high-fidelity refined flow field.

[0021] like Figure 5 As shown, a self-supervised three-dimensional particle tracking and velocimetry method includes the following steps: S1. Obtain the three-dimensional source particle set at time t in a continuous time series. The three-dimensional target particle set at time t+Δt By using SG-DGCNN, feature encoding is performed on the source particle set and the target particle set respectively to obtain the feature matrix of the corresponding particle set; S2. Input the feature matrices of the source particle set and the target particle set into DFCT, perform temporal alignment and semantic enhancement of the particle features of the two frames through DFCA, and output the aligned cross-frame features. S3. Based on the cross-frame features after alignment, the transmission cost matrix between particles is constructed through the optimal transmission theory. The global transmission plan is solved by the Sinkhorn algorithm to establish a dense soft correspondence between particles in two frames and output the initial flow field estimation results and matching confidence. S4. Construct a composite self-supervised loss function that integrates fluid physics constraints, and iteratively optimize the model parameters by minimizing the composite self-supervised loss function; S5. With the pre-trained model parameters frozen, the initial flow field estimation results are refined by iteratively optimizing the learnable residual flow tensor, and the final three-dimensional fluid velocity field is output.

[0022] It also includes S6, which uses three-dimensional fluid velocity field to perform flow field quantification analysis to determine the equipment structural design scheme.

[0023] In step S1, the three-dimensional source particle set at time t in the continuous time series is obtained. The three-dimensional target particle set at time t+Δt By using SG-DGCNN, feature encoding is performed on the source and target particle sets respectively, resulting in high-dimensional discriminative feature moments for the corresponding particle sets. Semantic features with both local geometric and topological information and high discriminative power are extracted from unstructured 3D particle point clouds, addressing the problems of insufficient feature representation capabilities and poor robustness to noise in existing methods.

[0024] S101, For each central particle in the particle set and its k nearest neighbor particles Construct a static geometry graph in three-dimensional coordinate space, for each edge Generate 6-dimensional composite geometric feature vectors , Integration from arrive 3D relative coordinates and Euclidean distance, and from observe The polar angle and azimuth angle spherical coordinate characteristics.

[0025] The feature extraction stage is implemented by constructing an SG-DGCNN. SG-DGCNN improves upon the geometric dynamic graph convolutional architecture by introducing self-learning pooling operators into the geometric graph convolutional layers, enhancing the edge feature representation capability of the edge convolutional layers, thereby enabling more effective learning of local graph features from the point cloud topology. Figure 2 As shown, SG-DGCNN employs a parallel dual-path design, using the original point cloud as input. (or target particle set) As input, a static geometry graph is first constructed using a geometry graph construction module to explicitly encode the spatial geometric relationships between particles. Subsequently, point cloud features are extracted simultaneously along two parallel paths: one is a geometric feature path containing a self-learning pooling operator, used to capture fine-grained spatial geometric properties; the other is a dynamic graph feature path, used to capture dynamic topological changes in the feature space. Finally, the multi-scale features from these two paths are concatenated and fused to generate a highly discriminative feature matrix. This serves as the input for subsequent cross-frame alignment modules.

[0026] Construct a static geometry graph for each central particle. and its k nearest neighbor particles Construct a static geometry graph in three-dimensional coordinate space, for each edge Generate 6-dimensional composite geometric feature vectors It integrates 3D relative coordinates, Euclidean distance, polar angle and azimuth spherical coordinate features.

[0027] When constructing the input for subsequent geometric extraction paths, SG-DGCNN employs a composite edge feature representation. This applies to the source particle set. (or target particle set) Any central particle in ) and Neighboring particles (in First, a geometric graph is constructed in the original three-dimensional coordinate space. This graph is for each edge. Generate a 6-dimensional geometric feature vector Its expression is:

[0028] In the above formula, It is 3D Cartesian coordinate interpolation, used as a 3D feature vector to represent the... arrive The relative position; It is Euclidean distance, representing and scalar distance between them; These are spherical coordinate features, representing respectively from observe The polar angle and azimuth angle.

[0029] These angles provide information about the relative layout of point pairs in different directions, and multidimensional geometric attributes provide information about the relative layout of point pairs in different directions. In the subsequent feature extraction module, the current features of each particle... and its neighbor characteristics It will be used to construct the edge feature input, by introducing the aforementioned 6-dimensional geometric information. It can encode the spatial and semantic relationships of neighborhood points more comprehensively and accurately, thereby enhancing the network's ability to understand the local dynamic characteristics of fluids.

[0030] S102. A parallel dual-branch architecture of geometric feature path and dynamic graph feature path is adopted. The geometric feature path extracts the spatial geometric attributes of particles through stacked geometric perception graph convolutional modules, while the dynamic graph feature path dynamically updates the k-NN graph in the feature space through serial dynamic edge convolutional layers to capture the semantic topological relationships of particles.

[0031] By using three stacked geometry-aware graph convolutional modules, a composite edge feature that integrates geometric features is constructed. After processing by a 1×1 convolutional layer, neighborhood feature aggregation is completed through a self-learning hybrid pooling strategy.

[0032] In the geometric feature extraction path, this embodiment achieves robust local geometric representation learning through three stacked geometry-aware map convolutional modules. In the processing of each layer, a central particle is first defined. The input feature vector is Its neighboring particles The feature vector is To enable the geometric context to effectively guide feature transformation, this embodiment calculates relative features. and combine it with pre-constructed 6D geometric features By performing concatenation along the channel dimension, composite edge features are constructed. ,in This represents the input feature dimension for this level. Subsequently, this composite edge feature is passed through a filter with activation and normalization functions. Convolutional layers are used to generate high-level feature representations. To overcome the limitations of fixed-rule pooling in preserving the integrity of local geometric information, this embodiment employs a self-learning pooling strategy based on a dynamic feature adjustment mechanism within the static graph convolutional layer. In this mechanism, two multilayer perceptrons are first used to process high-level features. Processing is performed to extract intermediate features. The calculation formula is as follows:

[0033] In the above formula, and Representing a linear layer, LeakyReLU represents a non-linear activation function. Next, the network proceeds along the neighbor dimension... Calculate attention weights:

[0034] Combine it with the original features Perform element-wise multiplication to obtain the optimized graph features. This dynamic adjustment mechanism allows the network to adaptively focus on important neighborhood features based on local context, effectively optimizing feature distribution and improving the relevance of aggregation. This is achieved by obtaining optimized graph features. Subsequently, this embodiment applies four different pooling methods in parallel to extract local features from multiple dimensions:

[0035] In the above formula, Represents batch index, Represents the feature channel index. Represents the particle number index. Represents the neighbor index. Max pooling. Capture the most significant features or peak information by extracting the maximum value along the neighbor dimension; mean pooling. By calculating the average value to reflect the overall evolution trend of neighborhood features; and pooling. By calculating the sum, the accumulated information within the neighborhood is aggregated, thereby comprehensively reflecting the cumulative effect of collective behavior in a sparse particle environment.

[0036] Furthermore, this embodiment introduces adaptive pooling. It is through a The convolutional kernel, combined with group normalization and the LeakyReLU activation function, enables the network to adaptively learn task-related local feature abstractions, capturing complex patterns that are difficult to recognize with traditional fixed pooling. Subsequently, this embodiment concatenates the feature vectors obtained from the above four pooling methods along the feature dimension to generate a wider fused feature vector.

[0037] Finally, the fused feature vector The feature representation is then fed into a feature fusion network consisting of two perceptron layers for compression and refinement, generating a more compact and highly discriminative final feature representation. This comprehensive pooling and fusion mechanism can extract rich features from the local point cloud topology more comprehensively and dynamically, thereby significantly improving the accuracy and robustness of fluid motion estimation in 3DPTV scenarios.

[0038] Two cascaded dynamic edge convolutional layers are used to dynamically update the k-NN graph in the feature space, capturing the semantic topological relationships in the feature space.

[0039] Complementing the fixed geometric path, the dynamic path in this embodiment is used to capture semantic topological relationships that evolve during feature learning. (See attached document.) Figure 2 As shown, this path follows the DGCNN architecture paradigm and employs two cascaded dynamic edge convolutional layers. The k-NN graph is dynamically updated in the feature space rather than the original coordinate space, which allows the model to cluster and associate semantically similar particles that are spatially far apart.

[0040] S103. The output features of different depths of the geometric feature path and the output features of the dynamic graph feature path are concatenated by channel dimension, and then compressed and refined by a multilayer perceptron to generate a 128-dimensional feature vector corresponding to each particle, forming a feature matrix.

[0041] To effectively integrate explicit spatial structure with dynamic feature correlation, this embodiment performs a multi-scale feature fusion operation, specifically by converting the geometric path into different depth outputs. Output of dynamic path generation The features are concatenated along the channel dimension to generate composite intermediate features. :

[0042] As a comprehensive descriptor encapsulating diverse geometric and topological abstraction information, it further undergoes feature projection and refinement through a hierarchical multilayer perceptron to compress rich feature information into a more compact and highly discriminative representation. Ultimately, it outputs a 128-dimensional basic feature vector for each input point, forming the final basic feature matrix. This basic feature matrix integrates multi-scale spatial structure information and dynamic semantic association information, serving as input for subsequent cross-frame feature alignment modules.

[0043] In step S2, the feature matrices of the source particle set and the target particle set are input into DFCT. DFCA is used to perform temporal alignment and semantic enhancement of the particle features of the two frames, and the aligned cross-frame features are output to solve the matching ambiguity problem in large displacement and high concentration flow fields, achieve accurate temporal alignment of particle features of the two frames, and significantly reduce the matching computation complexity.

[0044] DFCT is constructed by stacking multiple DFCA layers and a single FFN layer. It aims to improve the accuracy of fluid particle matching and flow field prediction by deepening the alignment of cross-frame features through iteration.

[0045] S201. For each particle in the query frame, first narrow the matching search range through spatial k-NN filtering, and then dynamically update the matching candidate set through feature similarity filtering to complete the two-layer candidate set filtering.

[0046] like Figure 3 As shown, the core design relies on a dynamic filtering mechanism for iterative alignment and the model learning capability of a cross-attention mechanism. In this embodiment, the module contains three cascaded DFCA layers. During the computation of each layer, query frame (Q-frame) features and key frame (K-frame) features serve as each other's inputs. For a given query particle, the spatial k-NN filtering remains relatively fixed during the computation, while the feature similarity filtering in the second stage dynamically changes as the features of each layer are updated; that is, the model re-evaluates and selects the most relevant matching candidate set at each layer. This dynamic filtering mechanism allows subsequent layers to gradually focus on more accurate semantic matching, thereby continuously improving matching quality and robustness during iteration. For the first... Q-frame input features of the layer and K-frame input features First, layer normalization is applied to obtain normalized features. and :

[0047] S202. Perform layer normalization on the feature matrices of the input source particle set and target particle set, and input the particle position information into the DFCA layer. The output of this layer is weighted by learnable scalar weights and then superimposed on the original input features through residual connections to generate intermediate features.

[0048] Subsequently, the normalized features , and its corresponding location information and The input is fed into the DFCA layer. The output of the DFCA layer is passed through learnable scalar weights. After weighting, the original input features are superimposed onto this layer through residual connections. and Above, generate intermediate features and :

[0049] In the above formula, This refers to the aforementioned DFCA layer, while These are learnable scalar weights. After completing the DFCA layer iterative processing, the intermediate features are... and Perform layer normalization again to obtain normalized intermediate features. and :

[0050] S203. After performing layer normalization on the intermediate features, input them into FFN. The output of FFN is weighted by learnable scalar weights and then superimposed onto the intermediate features through residual connections, outputting aligned cross-frame features.

[0051] Next, the normalized intermediate features are input into a standard two-layer FFN (consisting of a linear layer, a ReLU activation function, and a Dropout layer). The output of the FFN is then fed through learnable scalar weights. After weighting, the residuals are also superimposed onto the intermediate features. and This process is repeated to obtain the final alignment features. and :

[0052] DFCT allows the model to dynamically adjust the fusion strength and balance between newly acquired cross-frame context information and the original features of particles according to the needs of the learning task. Through this process, this embodiment can optimize the integration of cross-frame context information and the gain effect of nonlinear transformation while maintaining the stability of the original features.

[0053] In step S3, based on the cross-frame features after alignment, the transmission cost matrix between particles is constructed through optimal transmission theory. The global transmission plan is solved using the Sinkhorn algorithm to establish a dense soft correspondence between particles in two frames. The initial flow field estimation results and matching confidence are output. No ground truth label is required. The global dense soft correspondence between particles in two frames is established, and the initial flow field estimation is completed, providing a reliable mapping basis for self-supervised training.

[0054] S301. Based on the aligned cross-frame features, calculate the cosine similarity of features between the source and target particles. Define the optimal transmission cost using cosine similarity, construct the transmission cost matrix, and use the Sinkhorn algorithm to optimize the transmission plan between the two particle sets through entropy regularization and quality regularization. .

[0055] In this embodiment, the present invention employs a self-supervised learning paradigm to train the flow field estimation network, thereby completely eliminating the dependence on real label data. The core of this step lies in dynamically generating soft correspondences between particles using optimal transport theory, and constructing a composite self-supervised loss function to guide model optimization. First, to establish globally consistent and dense soft correspondences between two frames of point clouds, this embodiment uses optimal transport theory and the Sinkhorn algorithm, employing entropy regularization and quality regularization to optimize the transport plan between the particle sets of the two frames. Optimization will be performed. Among these optimizations, transmission costs are based on... and Features between cosine similarity To define.

[0056] S302. Calculate the soft correspondence weight of each source particle relative to the target particle based on the transport plan T. The predicted new position of the source particle is calculated by weighted averaging of the target particle's position. .

[0057] To differentiate it from the strong nonlinearity introduced by the standard Softmax exponentiation, the particles generated by the transport plan T... Compared to soft corresponding weights Obtained through the following normalization function:

[0058] In the above formula, express Zhongyu The set of candidate point indices corresponding to the maximum value. Based on this weight, the particle can be calculated. Predicting new location Its expression is:

[0059] S303. Based on the difference between the predicted new position and the original position of the source particle, calculate the initial flow field displacement vector, and at the same time calculate the confidence score of each pair of particles to complete the initial flow field estimation.

[0060] Meanwhile, this embodiment calculates the matching confidence score. The reliability of the predicted location for each pair of points is quantified for subsequent reconstruction loss calculation:

[0061] Ultimately, the estimated flow field (displacement term) Represented as .because It is based on the weighted average of the target frame particles, which is essentially a continuous estimate. This soft weighted averaging mechanism provides room for adjustment for subsequent test-time optimization.

[0062] In step S4, a composite self-supervised loss function integrating fluid physics constraints is constructed. The model parameters are iteratively optimized by minimizing the composite self-supervised loss function, thus eliminating the dependence on the truth label. The composite self-supervised loss function drives the model optimization while ensuring that the flow field results strictly conform to the laws of fluid physics.

[0063] S401. Construct a composite self-supervised loss function, and the total loss function. Reconstruction loss Flow field smoothing loss loss due to conservation of mass Weighted composition.

[0064] During model training, this embodiment minimizes the total loss function composed of multiple weighted loss terms. To optimize network parameters. The total loss function is defined as:

[0065] In the above formula, and It is a hyperparameter used to balance the weights of various loss terms. Specifically, reconstruction loss Used to measure the geometric consistency of point clouds, that is, the source point cloud after predicting flow field displacement should be highly similar to the target point cloud. The estimated flow field is used to transform the source point cloud... Transform into reconstructed point cloud ,in To estimate the flow field set.

[0066] S402. Calculate the reconstruction loss by calculating the geometric error between the reconstructed point cloud and the target point cloud after the predicted flow field transformation through the one-way chamfer distance. Combine the matching confidence weighting and introduce a regularization term to avoid degradation.

[0067] Through calculation and The unidirectional chamfer distance between them is used to minimize the reconstruction error, and a regularization term is introduced to prevent degeneracy. Its mathematical expression is:

[0068] In the above formula, The matching confidence level of the aforementioned optimal transmission output. To avoid Hyperparameters of trivial solutions.

[0069] S403. Calculate the smoothing loss, construct a spatial k-NN graph, and penalize each particle's flow field vector against its neighboring particle flow field vectors. Distance constrains the local spatial smoothness of the flow field.

[0070] To enhance the local smoothness and physical continuity of the estimated flow field, smoothing loss... This approach encourages a smooth spatial transition of the flow field by penalizing the difference between the flow field vector at each point and the flow field vectors at its neighbors. This embodiment constructs a spatial k-NN graph and computes the flow field vectors at each point. Flow field vector with his neighbors Flow field vector Average between distance:

[0071] In the above formula, Point The nearest neighbor set.

[0072] S404. Calculate the mass conservation loss by interpolating the point cloud flow field to a three-dimensional regular grid through inverse distance weighting, calculating the divergence of the grid flow field, and using the average of the absolute values ​​of the divergence of all grid points as the loss to constrain the physical law of mass conservation of incompressible fluids.

[0073] Furthermore, considering the characteristic that incompressible fluids must satisfy the law of mass conservation (i.e., sources or sinks with constant density and no abrupt changes), this embodiment introduces a mass conservation loss. The process first interpolates the point cloud flow field onto a regular 3D mesh. Then, the quality loss is quantified and penalized by calculating the divergence on that grid. Specifically, for point clouds... Each point in and its estimated flow field The flow field of the point cloud is mapped to the grid points using inverse distance weighting. Above, obtain the interpolated flow field :

[0074] In the above formula, Subsequently, the divergence of the flow field in the interpolated grid was calculated. The final mass loss is the average of the absolute values ​​of the divergence of all grid points:

[0075] Driven by the aforementioned composite self-supervised loss function, this embodiment can achieve geometrically consistent and physically reasonable flow field estimation results without the need for labeled data.

[0076] S405. Implement a step-by-step training strategy to decouple the model optimization process and avoid optimization conflicts caused by the instability of the feature extractor in the early stages of training.

[0077] S4051. In the first stage, SG-DGCNN is pre-trained. The original 3D coordinates are used as input, and the total loss function is minimized until convergence to obtain stable single-frame feature extraction capability.

[0078] To ensure the stability and optimization efficiency of feature extraction and alignment learning, this embodiment employs a step-by-step training strategy to decouple the model's optimization process. For the functionally decoupled architecture of this invention, the step-by-step strategy effectively avoids optimization conflicts caused by the instability of the feature extractor output in the early stages of training. The specific training and optimization process is as follows: During the training phase, the first stage of geometric feature extraction pre-training is performed. In this stage, SG-DGCNN is trained independently, using the original 3D coordinates as input, and by minimizing the aforementioned composite self-supervised total loss. Until convergence, the network is able to extract highly discriminative geometric features from a single frame of point cloud.

[0079] S4052. Second stage: Freeze the pre-trained network weights, train DFCT, focus on optimizing cross-frame feature interaction and alignment capabilities, and complete the overall model training.

[0080] The second stage of association learning is then performed, in which the weights of the pre-trained feature extractor are frozen to provide stable initial feature input for DFCT. At this stage, DFCT focuses on learning cross-frame feature interaction and alignment mechanisms to ensure that the downstream optimal transfer solver can receive accurate feature input, thereby improving the accuracy of the overall flow field estimation.

[0081] In step S5, under the premise of freezing the pre-trained model parameters, the initial flow field estimation results are refined by iteratively optimizing the learnable residual flow tensor, and the final three-dimensional fluid velocity field is output. This alleviates the difference in the distribution of training and test data, and further improves the fidelity of flow field estimation and the generalization ability of the model.

[0082] Furthermore, during the inference (testing) phase, to further enhance the model's generalization ability across different datasets and mitigate potential domain distribution differences, this embodiment introduces a test-time optimization mechanism. This mechanism is executed independently for each test instance, refining the flow field prediction results without updating the pre-trained network parameters. The specific optimization iteration process includes: S501. Initialize the residual stream: For each test instance, initialize a learnable residual stream tensor with all zeros. The initial flow field output by the pre-trained model Constructing a refined flow field The expression is as follows:

[0083] S502. Generate a reconstructed point cloud by using a refined flow field to transform the position of the source particle set. The expression is as follows:

[0084] S503. Strictly define the objective function as the reconstruction loss. Based on the gradient generated by the reconstruction loss, only the residual flow tensor... Perform backpropagation updates.

[0085] S504, based on the optimized refined flow field, outputs the final high-fidelity three-dimensional fluid velocity field.

[0086] because Initialized with zero residuals and with the chamfer distance providing clear gradient guidance, the process typically converges quickly within a short number of iterations (e.g., 100 steps). This mechanism effectively corrects the inherent reconstruction error in the optimal transport soft-weighted averaging process, significantly improving the fidelity of the flow field estimation and outputting a final high-fidelity three-dimensional fluid velocity field.

[0087] In step S6, a flow field quantification analysis is performed based on the three-dimensional fluid velocity field to determine the equipment structural design scheme, including the following steps: S601, derive the basic physical quantities of the flow field and perform data preprocessing.

[0088] Based on the final high-fidelity three-dimensional fluid velocity field output in step S5, the flow field derivative physical quantities are calculated and the data is standardized and preprocessed.

[0089] Based on the three-dimensional fluid velocity field, the core derivative physical quantities of the flow field, including vorticity field, strain rate tensor, turbulence intensity, etc., are calculated on the original particle point cloud and the interpolated three-dimensional regular mesh. At the same time, the calculation of physical quantities such as Reynolds stress, turbulence dissipation rate, wall shear stress, and velocity divergence is also completed.

[0090] By employing inverse distance weighting, Kriging interpolation, or finite element interpolation methods, the discrete velocity field in the form of unstructured particle point clouds is mapped into a continuous velocity field dataset of a three-dimensional structured regular mesh.

[0091] Based on the fundamental laws of fluid mass and momentum conservation, and combined with Gaussian filtering and median filtering, outliers and measurement noise in the flow field data are removed, data validity is verified, and a standardized flow field dataset is formed.

[0092] S602, Perform flow field quantitative analysis.

[0093] Based on a standardized flow field dataset, vortex identification methods such as the Q-criteria, λ²-criteria, and vortex amplitude are used to extract key flow structures such as vortex cores, vortex streets, shear layers, and flow separation zones from the three-dimensional velocity field, quantifying their spatial location, geometric dimensions, and temporal evolution. For turbulent flow fields, we calculate turbulence statistics such as velocity energy spectrum, probability density function, and spatial correlation function, analyze the multi-scale energy transfer law of turbulence, and compare the calculation results of large eddy simulation (LES) and direct numerical simulation (DNS) to verify and correct the theoretical deviation of the turbulence closure model.

[0094] S603. Based on the results of flow field quantitative analysis, determine the optimal equipment structure design scheme.

[0095] Based on three-dimensional velocity field data, the internal flow separation zone, secondary flow, dead zone, high loss region and flow instability structure of the equipment are located, and the core performance indicators such as the source of flow loss, flow field uniformity and energy conversion efficiency are quantified. To address the performance shortcomings identified through flow field diagnosis, and with the core objectives of reducing flow losses, improving energy efficiency, and enhancing operational stability, the geometric parameters of the equipment's flow-through components were modified.

[0096] For the optimized equipment structure, the flow field measurement and solution process of steps S1 to S5 is repeated to obtain the optimized three-dimensional velocity field. The flow field characteristics and performance indicators before and after optimization are compared. Through multiple rounds of iterative optimization, the optimal equipment structure design scheme is finally determined.

[0097] In the verification of real physical experimental data on flow around a cylinder, such as Figure 4 As shown, this invention successfully reconstructs a high-fidelity three-dimensional velocity field even without any truth labels, and accurately captures the complex wake structure and vortex street evolution behind the cylinder. Compared to traditional algorithms and existing self-supervised methods, the flow field estimated by this invention exhibits higher spatial resolution and physical coherence in regions with large velocity gradient changes.

[0098] Furthermore, in tests on various synthetic datasets, including isotropic turbulence, this invention maintained extremely low endpoint errors across different particle concentrations and displacement scales. Even in extremely scarce scenarios using only 1% of the training data, the prediction accuracy of this invention is comparable to supervised learning models trained on complete datasets, demonstrating superior data utilization efficiency. By integrating mass conservation physical constraints with test-time optimization mechanisms, this invention effectively corrects geometric reconstruction biases during optimal transmission and eliminates performance drops during cross-domain deployment. Experiments demonstrate that this invention not only exhibits significant robustness in handling complex flow fields with high density and large displacements, but also that the reconstruction results strictly adhere to fundamental laws of fluid mechanics, providing reliable technical support for accurate measurement of unsteady flow fields in industrial and scientific research scenarios.

[0099] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Clearly, those skilled in the art can make various alterations and variations to the invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of equivalents of the invention, the invention is also intended to include these modifications and variations.

Claims

1. A self-supervised three-dimensional particle tracking and velocity measurement method, characterized in that, Includes the following steps: S1. Obtain the three-dimensional source particle set and the three-dimensional target particle set in continuous time sequence. Use SG-DGCNN to encode the features of the source particle set and the target particle set respectively to obtain the feature matrix of the corresponding particle set. S2. Input the feature matrices of the source particle set and the target particle set into DFCT, perform temporal alignment and semantic enhancement of the particle features of the two frames through DFCA, and output the aligned cross-frame features. S3. Based on the cross-frame features after alignment, the transmission cost matrix between particles is constructed through the optimal transmission theory. The global transmission plan is solved by the Sinkhorn algorithm to establish a dense soft correspondence between particles in two frames and output the initial flow field estimation results and matching confidence. S4. Construct a composite self-supervised loss function that integrates fluid physics constraints, and iteratively optimize the model parameters by minimizing the composite self-supervised loss function; S5. With the pre-trained model parameters frozen, the initial flow field estimation results are refined by iteratively optimizing the learnable residual flow tensor, and the final three-dimensional fluid velocity field is output.

2. The self-supervised three-dimensional particle tracking and velocity measurement method according to claim 1, characterized in that, S1 includes the following steps: S101. For each central particle in the particle set and its k nearest neighbor particles, construct a static geometric graph in the three-dimensional coordinate space, and generate a 6-dimensional composite geometric feature vector for each edge formed by the central particle and the neighbor particles. The 6-dimensional composite geometric feature vector integrates the 3D relative coordinates from the central particle to the neighbor particles, the Euclidean distance between the central particle and the neighbor particles, and the polar angle and azimuth angle spherical coordinate features observed from the central particle to the neighbor particles. S102. A parallel dual-branch architecture of geometric feature path and dynamic graph feature path is adopted. The geometric feature path extracts the spatial geometric attributes of particles through stacked geometric perception graph convolutional modules, while the dynamic graph feature path dynamically updates the k-NN graph in the feature space through serial dynamic edge convolutional layers to capture the semantic topological relationships of particles. S103. The output features of different depths of the geometric feature path and the output features of the dynamic graph feature path are concatenated by channel dimension, and then compressed and refined by a multilayer perceptron to generate a 128-dimensional feature vector corresponding to each particle, forming a feature matrix.

3. A self-supervised three-dimensional particle tracking and velocity measurement method according to claim 2, characterized in that, In S102, a self-learning hybrid pooling strategy is used for neighborhood feature aggregation, including: For the composite edge features generated by the geometry-aware graph convolutional module, a high-level feature representation is obtained by processing them through a 1×1 convolutional layer. The attention weights of the neighborhood dimension are calculated by using two layers of multilayer perceptron and the Softmax function. The attention weights are then multiplied element-wise with the high-level feature representation to obtain the optimized graph features. Four pooling methods—max pooling, mean pooling, sum pooling, and adaptive pooling—are used in parallel to extract neighborhood-dimensional features from the optimized graph features. The features output by the four pooling methods are then concatenated along the channel dimension and compressed and refined by a feature fusion network to complete neighborhood feature aggregation.

4. The self-supervised three-dimensional particle tracking and velocity measurement method according to claim 1, characterized in that, In S2, DFCT consists of multiple cascaded DFCA layers and FFN stacks, employing a residual connection architecture; DFCA includes the following steps: S201. For each particle in the query frame, first narrow the matching search range by spatial k-NN filtering, and then dynamically update the matching candidate set by feature similarity filtering. S202. Perform layer normalization on the feature matrices of the input source particle set and target particle set, and input the particle position information into the DFCA layer. The output of the double-layer screening and cross-layer is weighted by learnable scalar weights and then superimposed on the original input features through residual connections to generate intermediate features. S203. After performing layer normalization on the intermediate features, input them into FFN. The output of FFN is weighted by learnable scalar weights and then superimposed onto the intermediate features through residual connections, outputting aligned cross-frame features.

5. A self-supervised three-dimensional particle tracking and velocity measurement method according to claim 1, characterized in that, S3 includes the following steps: S301. Based on the aligned cross-frame features, calculate the cosine similarity of features between the source particle and the target particle, define the transmission cost of optimal transmission with cosine similarity, construct the transmission cost matrix, and use the Sinkhorn algorithm to optimize the transmission plan between the two-frame particle sets through entropy regularization and quality regularization. S302. Calculate the soft correspondence weight of each source particle relative to the target particle based on the transmission plan, and calculate the predicted new position of the source particle by weighted average of the target particle positions. S303. Based on the difference between the predicted new position and the original position of the source particle, calculate the initial flow field displacement vector, and at the same time calculate the confidence score of each pair of particles.

6. A self-supervised three-dimensional particle tracking and velocity measurement method according to claim 1, characterized in that, In S4, the total loss function of the composite self-supervised loss function is the sum of the reconstruction loss, the weighted flow field smoothing loss, and the weighted mass conservation loss.

7. A self-supervised three-dimensional particle tracking and velocity measurement method according to claim 6, characterized in that, The reconstruction loss is obtained by calculating the one-way chamfer distance between the reconstructed point cloud after the predicted flow field transformation and the target point cloud, combined with the matching confidence weighting, and a regularization term is introduced; The flow field smoothing loss is calculated by constructing a spatial k-NN graph and averaging the flow field vector of each particle with the flow field vectors of its neighboring particles. The distance is obtained and used to constrain the local spatial smoothness of the flow field; The mass conservation loss is calculated by interpolating the point cloud flow field to a three-dimensional regular grid through inverse distance weighting, and then calculating the divergence of the grid flow field. The average of the absolute values ​​of the divergence of all grid points is used to constrain the physical law of mass conservation of incompressible fluids.

8. A self-supervised three-dimensional particle tracking and velocity measurement method according to claim 1, characterized in that, In S4, model training employs a step-by-step training strategy, including: In the first stage, SG-DGCNN is trained independently. The original three-dimensional particle coordinates are used as input, and the feature extractor is pre-trained by minimizing the composite self-supervised loss function until convergence. In the second stage, the weights of the pre-trained SG-DGCNN are frozen, and DFCT is trained. The cross-frame feature alignment capability is optimized by minimizing the composite self-supervised loss function, thus completing the training of the overall model.

9. A self-supervised three-dimensional particle tracking and velocity measurement method according to claim 1, characterized in that, S5 includes the following steps: S501. For each test instance, initialize a learnable residual flow tensor with all zeros, and construct a refined flow field by combining the initial flow field output by the pre-trained model. S502. The source particle set is transformed using a refined flow field to generate a reconstructed point cloud. S503. Using reconstruction loss as the objective function, backpropagation is used to iteratively update only the residual flow tensor until convergence. S504: Based on the optimized refined flow field, output the final three-dimensional fluid velocity field.

10. A self-supervised three-dimensional particle tracking and velocimetry method according to claim 1, characterized in that, Also includes: S6. Perform flow field quantification analysis based on three-dimensional fluid velocity field to determine the equipment structural design scheme.

Images