A vortex reconstruction and tracking method, device and storage medium

Abstract

The application provides a vortex reconstruction and tracking method, aiming at the defects of the traditional vortex reconstruction method in three-dimensional sampling, pseudo matching suppression and the like, the application effectively matches vortex axes in three-dimensional directions, takes into account the three-dimensional sampling effect, and has a better reconstruction effect on isotropic vortices; meanwhile, by using the constraint characteristics of the vector direction of Liutex, physical constraint conditions during matching are set, the phenomenon of pseudo vortex axis point matching is effectively reduced; by using a graph neural network and reinforcement learning, vortex axis matching is optimized, three-dimensional reconstruction precision is improved, and pseudo matching is suppressed by global topological constraints; by extracting vortex axis points with dominant absolute rotation intensity, changes in the structure of a single vortex when evolving over time in a flow field are intuitively observed.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of fluid mechanics, and particularly relates to a vortex reconstruction and tracking method, device and storage medium. BACKGROUND

[0002] Vortex is the main cause of turbulent fluctuations, and plays a key role in the generation and maintenance of turbulence. Accurate identification of vortex structure is of great significance for understanding flow mechanism, solving turbulence problems and flow control.

[0003] In order to identify the vortex structure in the flow field, researchers have proposed many vortex identification criteria. The first generation method regards the anti-symmetric part of the velocity gradient tensor (vorticity tensor) obtained by Cauchy-Stokes decomposition as rotation, but it is abandoned because it cannot distinguish between rotational motion and pure shear. The second generation vortex identification method represented by Q (the second Galilean invariant of the velocity gradient tensor), λ2 (the second eigenvalue of the symmetric tensor), Δ (the discriminant of the velocity gradient tensor), λ ci The second generation vortex identification method can greatly improve the vortex identification effect, but it can only mark the spatial region belonging to the vortex, and cannot provide information about the topological structure and shape of a single vortex. Currently, some scholars have proposed a VATIP (Vortex axis tracking by iterative propagation) algorithm based on the second generation vortex identification method. The algorithm propagates along the vortex axis and iteratively searches for new growth directions, and can controllably generate vortexes of different shapes in the instantaneous simulation flow field. However, the method has the following three defects:

[0004] (1) The VATIP algorithm only initializes the vortex axis by searching in the flow direction, and only adds propagation points to the existing vortex axis in the vertical and spanwise directions to extend the two direction axes, and does not start a new vortex from any isolated axis point. This makes the generated axis only have good sampling effect in the flow direction, and ignores the sampling in the vertical and spanwise directions, resulting in poor reconstruction effect of isotropic vortexes that are away from the wall.

[0005] (2) In a fully developed turbulent flow field, the axes of different vortexes often come into close contact, but spatial proximity does not necessarily mean matching. The VATIP algorithm does not set physical constraints for this, and it will inevitably incorrectly match the axes that do not belong to the same vortex structure.

[0006] (3) The current VATIP algorithm can only generate vortexes based on the instantaneous flow field, and cannot track the morphological changes of vortexes over time and space.

[0007] The above defects show that the traditional vortex reconstruction method faces great challenges in dealing with three-dimensional sampling, pseudo-matching suppression and cross-space-time tracking, and with the rapid development of artificial intelligence technology, the flow field analysis method based on machine learning and deep learning gradually shows unique advantages in extracting complex flow characteristics. Therefore, it is urgent to develop a vortex reconstruction and tracking method that combines artificial intelligence technology, can consider three-dimensional sampling effect, reduce false vortex axis point error matching, and track single vortex morphology across time, to provide multi-scale, cross-space-time and high-precision vortex reconstruction and tracking method for studying vortex dynamics and turbulent self-regeneration mechanism. SUMMARY

[0008] The present application aims to at least partially solve one of the technical problems in the related art.

[0009] To this end, the present application provides a vortex reconstruction and tracking method, device and storage medium, which can reduce the error matching probability of false vortex axis points and track single vortex across time while considering three-dimensional sampling effect and reconstruction speed.

[0010] To achieve the above purpose, the present application adopts the following technical solutions:

[0011] The present application provides a vortex reconstruction and tracking method in the first aspect, comprising the following steps:

[0012] Step S100, acquiring the instantaneous three-dimensional flow field data in each time t N i Assigning index numbers to each plane parallel to the x, y and z directions, for each time t i , calculating the vortex absolute intensity value R, the direction r of the vortex absolute intensity vector Liutex and the vortex relative intensity value OmegaR of each grid point in the three-dimensional flow field, and obtaining the feature vector of each grid point in combination with the position and instantaneous flow rate of the grid point, and initializing the vortex number in each minimum index number plane based on the feature vector of each grid point; constructing an undirected graph G id1_id2 based on the feature vectors of the 9-neighborhood extreme points of the vortex absolute intensity value R in the adjacent two planes at the same time and parallel to each other, and the index numbers of the two adjacent planes used when constructing the undirected graph are represented by the subscripts id1 and id2 respectively;

[0013] Step S200, inputting all undirected graphs at time t i and the initial vortex number into the pre-trained graph neural network, and the graph neural network predicts the matching relationship of the vortex axis based on the topological consistency, supervised learning and isotropic criteria to obtain the initial set A i of vortex axis at time t GNN_i ; inputting A GNN_i ​In the input pre-trained reinforcement learning model, the reinforcement learning model suppresses false matches in A GNN_i based on the direction consistency and intensity continuity criteria, to obtain a vortex axis optimization set A i at time t opt_i ; A GNN_i and A opt_i respectively record the number of each vortex and the feature vector of each vortex at different vortex axis points;

[0014] Step S300, starting from time period t1-t2, sequentially performing single-vortex tracking on each time period t i -t i+1 in chronological order until time period t N-1 -t N , to obtain a vortex tracking sequence at tracking time t1-t N The single-vortex tracking process for time period t i -t i+1 includes:

[0015] Iterate through all the vortices at time t i to sequentially take each vortex as a target vortex, extract the vortex axis point with dominant vortex absolute intensity value R based on the information of the target vortex in A opt_i , and take it as a tracking point, predict the position and velocity of the tracking point at time t i+1 , and determine whether the target vortex dissipates at time t i+1 . If not, it is determined that the target vortex is successfully tracked, and the origin time of the target vortex is marked as time t i+1 ;

[0016] Statistically, each vortex with the same vortex number and successfully tracked within tracking time t1-t N is taken as a vortex tracking sub-sequence, and all vortex tracking sub-sequences constitute a vortex tracking sequence at tracking time t1-t N

[0017] In some embodiments, in step S100, the initialization of the vortex number in each minimum index number plane based on the feature vector of each grid point includes:

[0018] Iterate through all grid points in the three-dimensional flow field at each time within tracking time t1-t N , set the value of OmegaR<θ1 to 0, obtain different sizes of OmegaR clusters in the processed three-dimensional flow field, and each cluster represents a vortex with clear boundaries, θ1 is the first threshold value;

[0019] Iterate through all grid points in the three-dimensional flow field at each time within tracking time t1-t N ​​All OmegaR clusters in the three-dimensional flow field at each time are screened, and clusters with less than 3 grid points in the x, y and z directions are considered as noise points, and the values are set to 0 to obtain the denoised OmegaR;

[0020] According to the grid points equal to 0 in the denoised OmegaR, the corresponding position of the vortex absolute intensity value R is set to 0 to obtain the processed R;

[0021] For the processed R, different vortex numbers are assigned to each 9-neighborhood extreme point in each minimum index number plane as a reference point. When the reference point is a 9-neighborhood extreme point in multiple directions, the vortex number in the x direction is selected as the priority, followed by the vortex number in the y direction and the vortex number in the z direction. Then, according to the direction r of the Liutex of all reference points in each minimum index number plane, the initialization of the vortex number in each minimum index number plane is completed.

[0022] In some embodiments, in step S100, the undirected graph G id1_id2 is constructed by the following steps:

[0023] Tracing the time t1~t N at each time and parallel to each other, for the id1th and id2th planes at time t i , first determine the 9-neighborhood extreme points of each vortex absolute intensity value R in the id1th and id2th planes; then divide the 9-neighborhood extreme points in the id1th plane into a reference node V m , and divide the 9-neighborhood extreme points in the id2th plane into a to-be-matched node, and normalize the feature vectors of each node to [0, 1] to obtain the normalized feature vectors of each node;

[0024] When the spatial distance between the reference node V max and the to-be-matched node V m is less than the set maximum connection distance d n , an edge E mn is constructed between them;

[0025] The edge weight w mn is set based on distance and direction consistency:

[0026]

[0027] where σ d is a distance scale parameter for controlling the sensitivity of distance to edge weight; σ θ is a direction scale parameter for controlling the sensitivity of direction angle to edge weight; is a reference node V mLiutex direction r m and the node to be matched V n Liutex direction r n between the two, r mx , r my , r mz are three-dimensional vector components of r m , r nx , r ny , r nz are three-dimensional vector components of r n ;

[0028] According to the set nodes and edges, an undirected graph G id1_id2 is obtained

[0029] G id1_id2 = (V id1_id2 , E id1_id2 )

[0030] wherein V id1_id2 is a node set of the undirected graph G id1_id2 , and E id1_id2 is an edge set of the undirected graph G id1_id2 .

[0031] In some embodiments, the training process of the graph neural network comprises:

[0032] Step S211, first training sample set construction:

[0033] Step S2111, obtaining the instantaneous three-dimensional flow field data at each time τ k in the continuous time τ1~τ K , assigning each plane parallel to the x, y, and z directions in the three-dimensional flow field with the same index number as the corresponding plane in step S100, calculating the vortex absolute intensity value R, the direction r of the vortex absolute intensity vector Liutex, and the vortex relative intensity value OmegaR of each grid point in the three-dimensional flow field for each time τ k , and obtaining the feature vector of each grid point in combination with the position and instantaneous flow rate of the grid point, and initializing the vortex numbering in each minimum index number plane based on the feature vector of each grid point;

[0034] Step S2112, for each time τ k in the continuous time τ1~τ K , the following method is used to obtain the corresponding vortex three-dimensional multi-direction reconstruction result:

[0035] According to τ kThe current vortex information of each minimum index number plane is recorded, and the positive and negative bidirectional reconstruction of the vortex is sequentially performed in the x, y and z directions with the constraint condition of matching the nearest prediction point in priority, the position of the prediction point is calculated by the constraint of the direction r of Liutex, the current vortex quantity is counted, the current round of three-dimensional multi-directional reconstruction of the vortex is ended, and the above steps are performed for multiple rounds of three-dimensional multi-directional reconstruction of the vortex, when the vortex quantity converges, the τ k The three-dimensional multi-directional reconstruction of the vortex is recorded at each moment k The number and characteristic vector of all the vortexes at each moment are recorded as τ k The three-dimensional multi-directional reconstruction result of the vortex at each moment

[0036] In step S2113, according to the three-dimensional multi-directional reconstruction result of the vortex at K moments obtained in step S2112, an undirected graph is constructed based on the characteristic vectors of vortex axis points in adjacent two planes parallel to each other at the same moment Each constructed undirected graph is taken as a first training sample All first training samples are taken as a first training sample set

[0037] In step S212, a graph neural network is constructed and trained

[0038] An L-layer graph neural network is adopted, the first training sample is input into the graph neural network, and a corresponding vortex axis prediction set A is obtained GNN_k Wherein, the embedding vectors of all nodes in the input first training sample are updated by using the graph neural network, and the update process is as follows:

[0039] h e (l+1) =ReLU(W (l) ·MEAN({h g (l) |g∈N(g)})+B (l) h e (l) )

[0040] Wherein, h e (l) and h g (l) are embedding vectors generated by the graph neural network at the lth layer for nodes V e and nodes Vgrespectively, nodes V e and nodes V g are two nodes with edges in the undirected graph N(g) is the neighborhood of node V e W (l) and B (l)Here, represents the weight matrix and bias vector of the l-th layer of the graph neural network; ReLU is the activation function used in the hidden layer of the graph neural network; MEAN is the mean aggregation function.

[0041] For each pair of nodes (V) e V g ), Graph neural networks use their output layer to predict node V e With node V g Matching tags The prediction process is as follows:

[0042]

[0043] in, Through node V e With node V g The probability of belonging to the same vortex is represented; Sigmold is the activation function used in the output layer of the graph neural network; W out b is the linear transformation matrix of the weights of the output layer of the graph neural network; out This is the offset;

[0044] For undirected graphs All nodes V e Predicting V using the output layer of a graph neural network e pseudo-matching tags

[0045]

[0046] in, Using node V e Characterize the probability of spurious matching points; W pscudo b is the weight matrix for pseudo-match prediction; pscudo The bias scalar for the pseudo-match prediction;

[0047] Set the loss function L for the graph neural network. GNN :

[0048]

[0049] Among them, L ce The cross-entropy loss function is y. eg Node V is set based on the vortex 3D reconstruction result corresponding to the first training sample. e With node V g True match tags; z e Node V is set based on the vortex 3D reconstruction result corresponding to the first training sample. e The true and false matching labels are λ, the false matching loss weights are μ, the orientation constraint weights are E, and E is the set of edges of the input undirected graph. the angle between the Liutex direction r of the node V e e and the Liutex direction r of the node V g g .

[0050] In some embodiments, when a single round of vortex multi-direction reconstruction is performed in step S2112, first, the vortex information of each minimum index number plane at time τ k is used to sequentially perform positive and negative direction reconstruction of the vortex in the x, y, and z directions, and then the number of vortexes in the three-dimensional flow field is counted; when positive direction reconstruction is performed, the two adjacent planes are sequentially matched in a positive direction according to the order of the index numbers from small to large, until the maximum index number plane and the minimum index number plane are positively matched, and then the two adjacent planes are sequentially matched in a negative direction according to the order of the index numbers from large to small, until the minimum index number plane and the maximum index number plane are negatively matched; wherein, for the two adjacent planes to be matched,

[0051] For positive direction matching, 9-neighborhood extreme points that have been assigned vortex numbers are selected from the plane with a smaller index number as reference points, the projection positions of each reference point in the plane with a larger index number are predicted using the positive normalized value of the component of the Liutex direction r to obtain the corresponding matching points, and the matching points are assigned the same vortex numbers as the reference points; for 9-neighborhood extreme points in the plane with a larger index number that have not been assigned vortex numbers and have a component of the Liutex direction r greater than 0, new vortex numbers are assigned to them.

[0052] For negative direction matching, each 9-neighborhood extreme point with a component of the Liutex direction r less than 0 is selected from the plane with a larger index number as a reference point, and new vortex numbers are assigned to reference points that have not been assigned vortex numbers, the projection positions of each reference point in the plane with a smaller index number are predicted using the negative normalized value of the component of the Liutex direction r to obtain the corresponding matching points, and the matching points are assigned the same vortex numbers as the reference points; for 9-neighborhood extreme points in the plane with a smaller index number that have not been assigned vortex numbers and have a component of the Liutex direction r less than 0, new vortex numbers are assigned to them.

[0053] In some embodiments, in step S200, the graph neural network predicts the matching relationship of the vortex axis line, specifically including:

[0054] all undirected graphs in three directions at time t i are input into the graph neural network in three batches, all undirected graphs in the same direction and the initialized vortex numbers are input in each batch, then the graph neural network performs positive and negative direction matching on all undirected graphs input in the same batch to obtain the matching relationship of the vortex axis line at time t​​i The initial set A of vortex axes at time t. GNN_i It includes matching relationships in all directions, specifically:

[0055] For positive matching in the x-direction: starting from the yz plane with the smallest index number, matching is performed in ascending order of plane index numbers, for the undirected graph G of the input graph neural network between the id_x-th and id_x+1-th yz planes. (id_x)_(id_x+1) For the node V in the undirected graph that has been assigned a vortex number m The graph neural network predicts matching nodes V n If node V m Matching node V n Matching tags Then assign the matching node V n With node V m The same vortex number, θ connect The set probability threshold is used; otherwise, it is G. (id_x)_(id_x+1) The unnumbered component r of the Liutex direction in the x-direction. x Nodes with a value greater than 0 are assigned a new number; id_x is updated and iterated until the yz plane with the largest index number and the yz plane with the smallest index number complete a positive matching prediction;

[0056] For negative matching in the x-direction: starting from the yz plane with the largest index number, filter r in descending order of plane index numbers. x For nodes less than 0, input the undirected graph G in the yz plane between the id_x-th and id_x-1-th nodes. (id_x)_(id_x-1) Regarding the graph neural network, for the node V in the undirected graph that has been assigned a vortex number... m The graph neural network predicts matching nodes V n If node V m Matching node V n Matching tags Then assign the matching node V n With node V m The same vortex number; otherwise, it is an undirected graph G. (id_x)_(id_x-1) Unnumbered and r x Nodes with a value less than 0 are assigned a new number; id_x is updated and iterated until the yz plane with the smallest index number and the yz plane with the largest index number complete a negative matching prediction;

[0057] Referring to the matching process in the x-direction, positive and negative matching predictions are performed sequentially in the y-direction and z-direction;

[0058] Finally, nodes with pseudo-matching labels greater than the set threshold are removed, the matching relationship is updated, and t is obtained. i The initial set A of vortex axes at time t. GNN_i.

[0059] In some embodiments, step S200, the training process of the reinforcement learning model includes:

[0060] Step S231, Construction of the second training sample set:

[0061] The vortex axis prediction set A obtained from step S212 will be used. GNN_k and with A GNN_k The corresponding graph neural network has node V in layer L. e The generated embedding vector h e (L) Node V e With node V g Matching tags and each node V e pseudo-matching tags Together they form a second training sample, and the second training sample set is constructed from all the second training samples.

[0062] Step S232, RL model environment construction:

[0063] In the τth step of making a decision for the reinforcement learning model, node V... e normalized eigenvector f' e The graph neural network has node V in layer L. e The generated embedding vector h e (L) splicing to form state s τ Define action a τ ={a1,a2,a3,a4,a5,a6,a7}, where a1 and a2 represent positive and negative matching in the x direction, respectively; a3 and a4 represent positive and negative matching in the y direction, respectively; a5 and a6 represent positive and negative matching in the z direction, respectively; and a7 represents terminating the matching and assigning a new vortex number.

[0064] Define reward function r τ :

[0065]

[0066] Among them, R max R is the largest absolute vortex intensity among all second training samples. e and R g They are nodes V e and node V g The absolute intensity value of the vortex;

[0067] Step S233, Reinforcement Learning Model Design and Training:

[0068] Define the reinforcement learning model as an L-layer multilayer perceptron, with state s as its input. τ The output is a 7-dimensional motion a τ The probability is determined by the proximity policy optimization algorithm used in the reinforcement learning model, and the objective function is set as J(θ). RL ):

[0069]

[0070] in, To calculate the expected value of the function; ε τ Let θ be the discount factor at step τ. RL These are the network parameters of the reinforcement learning model;

[0071] The reinforcement learning model predicts the vortex axis set A in the second training sample according to the following steps. GNN_k Iterative optimization is performed:

[0072] When performing the initial optimization of the reinforcement learning model, A is used GNN_k Initialize the reference node V e ∈A GNN_k In subsequent optimizations, the output of the previous reinforcement learning model is used to initialize each baseline node for the next optimization.

[0073] For each direction x, y, z: input state s τ Predict action a τ ;

[0074] If a τ To perform the matching operation, direction consistency is required. Matching nodes V predicted by the neural network for intensity continuity check graph g And calculate the reward r τ If a τ To terminate the operation, the current reference node V is selected. e Assign new vortex numbers; update the feature vector and graph neural network embedding vector by switching to the next node, record the plane index number and vortex number, and update the state s. τ The iteration continues until all nodes have completed vortex numbering, the number of vortices at the end of this iteration is counted, and the next reinforcement learning optimization begins.

[0075] When the number of vortices obtained from consecutive reinforcement learning iterations becomes stable, the iteration stops and τ is output. k Optimization set A of vortex axis at time moment opt_k .

[0076] In some embodiments, step S300 specifically includes:

[0077] Step S310, Single vortex tracking during time period t1~t2:

[0078] The optimized set A of vortex axes at time t1 obtained in step S200 opt_1 All vortices in the time period t1 to t2 starting time t1 are sequentially tracked as target vortices, specifically as follows:

[0079] Step S311: Optimize the vortex axis set A based on time t1. opt_1 The absolute vortex intensity values ​​R of all vortex axis points on the current target vortex are sorted from largest to smallest. The top B vortex axis points are taken as the absolute rotation intensity points and recorded as tracking points. The feature vector of each tracking point is recorded.

[0080] Step S312: Calculate the predicted position P of each tracking point at time t2 according to the following formula. predicted :

[0081] P predicted =P current +V·Δt

[0082] In the formula: P current = (x,y,z), is the position of the tracking point at time t1, V = (u,v,w) is the velocity of the tracking point at time t1, and Δt is the duration between two adjacent time points;

[0083] For each tracking point, define its own rectangular search range, taking η times the displacement of the corresponding tracking point:

[0084] X range =[X predicted -η·|u·Δt|,X predicted +η·|u·Δt|]

[0085] Y range =[Y predicted -η·|v·Δt|,Y predicted +η·|v·Δt|]

[0086] Z range =[Z predicted -η·|w·Δt|,Z predicted +η·|w·Δt|]

[0087] In the formula: X range Y range and Z range These represent the search ranges of a given tracking point in the x, y, and z directions, respectively; X predicted Y predicted and Z predicted These are the predicted positions of a certain tracking point in the x, y, and z directions at time t2, respectively.

[0088] Step S313, based on the vortex axis line optimization set A at t2 opt_2 In the rectangular search range corresponding to each tracking point, if the ratio of the number B' of vortex axis points with the same vortex number searched to B is greater than the fourth threshold θ4, it is considered that the vortex is a successfully tracked vortex, and the time label of the vortex is marked as t1, otherwise it is considered that the vortex has dissipated at t2. After tracking all the vortexes at t1, the vortexes at t2 without time label are marked as t2, and it is considered that the vortex originates from t2. Thus, the single vortex tracking of the time period t1-t2 is completed.

[0089] Step S320, according to steps S311-S313, sequentially track the single vortex of each time period t2-t2,...,t i i+1 N-1 N ...

[0090] Step S330, count the vortexes with the same vortex number and successfully tracked in the tracking time t1-t N , respectively as a vortex tracking subsequence, and all vortex tracking subsequences constitute the vortex tracking sequence of the tracking time t1-t N

[0091] The vortex reconstruction and tracking device provided in the second aspect of the present application comprises:

[0092] The first module is configured to obtain the instantaneous three-dimensional flow field data at each time t N in the tracking time t1-t i , respectively assign index numbers to each plane parallel to the x, y, and z directions, calculate the vortex absolute intensity value R, the direction r of the vortex absolute intensity vector Liutex, and the vortex relative intensity value OmegaR of each grid point in the three-dimensional flow field for each time t i , and obtain the feature vector of each grid point by combining the position and instantaneous flow rate of the grid point. The vortex number of each minimum index number plane is initialized based on the feature vector of each grid point. The feature vectors of the 9-neighborhood extreme points of each vortex absolute intensity value R in the adjacent two planes at the same time and parallel to each other are used to construct an undirected graph G id1_id2 , and the subscripts id1 and id2 represent the index numbers of the two adjacent planes used to construct the undirected graph.

[0093] The second module is configured to mark the vortexes at t i ​​​​all the undirected graphs at time t and the initial vortex number input into a pre-trained graph neural network, the graph neural network predicts the matching relationship of the vortex axis based on topological consistency, supervised learning and isotropic criteria, to obtain A i the initial set of vortex axis at time t GNN_i ; A GNN_i is input into a pre-trained reinforcement learning model, the reinforcement learning model suppresses the pseudo-matching in A GNN_i based on the direction consistency and intensity continuity criteria, to obtain A i the optimized set of vortex axis at time t opt_i ; A GNN_i and A opt_i respectively record the number of each vortex and the feature vector of each vortex at different vortex axis points;

[0094] The third module is configured to sequentially perform single-vortex tracking on each time period t i ~t i+1 in chronological order from time period t1~t2, until time period t N-1 ~t N , to obtain a vortex tracking sequence at tracking time t1~t N The single-vortex tracking process for time period t i ~t i+1 includes:

[0095] Iterate through all the vortexes at time t i , and sequentially take each vortex as a target vortex, extract the vortex axis point with dominant vortex absolute intensity value R based on the information of the target vortex in A opt_i , and take it as a tracking point, predict the position and velocity of the tracking point at time t i+1 , and determine whether the target vortex is dissipated at time t i+1 , if not, it is determined that the target vortex is successfully tracked, and the origin time of the target vortex is marked as time t i+1 ;

[0096] Statistically, each vortex with the same vortex number and successfully tracked within tracking time t1~t N is taken as a vortex tracking sub-sequence, and all vortex tracking sub-sequences constitute a vortex tracking sequence at tracking time t1~t N .

[0097] The third aspect of the present application provides a computer readable storage medium, the computer readable storage medium stores computer instructions, the computer instructions are used to make the computer execute the vortex reconstruction and tracking method according to any one of the embodiments of the first aspect of the present application.

[0098] ​Compared with the prior art, the present application has the following characteristics and beneficial effects: compared with the existing VATIP algorithm based on the second generation vortex identification criterion, the embodiment of the present application effectively matches the vortex axis in three-dimensional directions, allows the vertical and spanwise isolated axis points to start matching new vortexes, takes into account the three-dimensional sampling effect, has better reconstruction effect on isotropic vortexes, and effectively improves the vortex reconstruction rate; meanwhile, through the constraint characteristics of the vector direction of Liutex, the physical constraint condition during matching is set, the phenomenon of matching of pseudo-vortex axis points connected due to similarity is effectively reduced; meanwhile, the vortex axis matching is optimized by using the graph neural network and reinforcement learning, the three-dimensional reconstruction precision is improved, and the pseudo-matching is inhibited through global topological constraint; through extraction of the vortex axis points with absolute rotation intensity dominance, cross-time tracking of single vortexes is realized, the structural changes of single vortexes in the flow field when evolving over time can be directly observed, and the method provides a new multi-scale, cross-time-space and high-precision analysis paradigm for studying vortex dynamics and self-regeneration mechanism of turbulence. BRIEF DESCRIPTION OF DRAWINGS

[0099] Figure 1 is a flow chart of a vortex reconstruction and tracking method provided by the embodiment of the present application;

[0100] Figure 2 is a schematic diagram of vortex x direction reconstruction and matching of the reconstruction and tracking method provided by the embodiment of the present application;

[0101] Figure 3 is a vortex visualization schematic diagram of the flow field after three-dimensional bidirectional reconstruction by the embodiment of the present application;

[0102] Figure 4 is a schematic diagram of cross-time-space tracking of single vortexes by the reconstruction and tracking method provided by the embodiment of the present application;

[0103] Figure 5 is a structural schematic diagram of an electronic device provided by the embodiment of the present application. DETAILED DESCRIPTION

[0104] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application is further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0105] On the contrary, the present application covers any alternative, modification, equivalent method and scheme defined by the claims on the essence and scope of the present application. Further, in order to make the public better understand the present application, some specific details are described in detail in the following detailed description of the present application. The present application can also be completely understood without the description of these details by those skilled in the art.

[0106] Referring to Figure 1 , the vortex reconstruction and tracking method provided by the embodiment of the present application comprises the following steps:

[0107] Step S100, acquiring instantaneous three-dimensional flow field data of each time t N i The time length of adjacent two time points is equal. Index numbers are respectively assigned to each plane parallel to the x, y and z directions. For each time t i , the absolute vortex intensity value R, the direction r of the absolute vortex intensity vector Liutex and the relative vortex intensity value OmegaR of each grid point in the three-dimensional flow field are calculated to obtain the 11-dimensional feature vector of each grid point, including the three-dimensional position, the three-dimensional instantaneous flow velocity, the three-dimensional vector component of the direction r of R and OmegaR, and the initialization of the vortex numbering in each minimum index number plane is completed based on the 11-dimensional feature vector of each grid point; the 11-dimensional feature vector of the 9-neighborhood extreme point of each vortex absolute intensity value R in the adjacent two planes at the same time and parallel to each other is used to construct an undirected graph G id1_id2 , and the subscripts id1 and id2 respectively represent the index numbers of the two adjacent planes used when constructing the undirected graph;

[0108] Step S200, inputting all undirected graphs at time t i and the initial vortex numbering into a pre-trained graph neural network (GNN), and the GNN predicts the matching relationship of the vortex axis based on the topological consistency, supervised learning and isotropic criteria. Specifically, the probability that the matching node and the vortex number node assigned belong to the same vortex is predicted. If the probability is greater than a probability threshold, the matching node is given the same vortex number, so as to obtain the initial set A i of vortex axis at time t GNN_i ; inputting A GNN_i into a pre-trained reinforcement learning (RL) model, and the RL model suppresses the pseudo-matching in A GNN_i based on the direction consistency and intensity continuity criteria to obtain the optimized set A i of vortex axis at time t opt_i ; A GNN_i and A opt_i respectively record the numbering of each vortex and the 11-dimensional feature vector of each vortex at different vortex axis points;

[0109] Step S300, starting from the time period t1-t2, sequentially performing single-vortex tracking on each time period t i -t i+1 until the time period t N-1 -t N , to obtain the vortex tracking sequence at the tracking time t1-t N ​​ for the time period t i ~t i+1 The single-vortex tracking process of each vortex at time t

[0110] for the time period t i Each vortex at time t opt_i is sequentially taken as a target vortex, and the vortex axis point with the largest absolute intensity value R of the target vortex at time t i+1 is extracted based on the information of the target vortex at time t i+1 and is taken as a tracking point. The position and velocity of the tracking point at time t i+1 are predicted, and it is determined whether the target vortex at time t N is dissipated. If the target vortex is not dissipated, it is determined that the target vortex is successfully tracked, and the time t N is marked as the origin time of the target vortex.

[0111] The tracking time t1~t N is divided into a plurality of time periods, each time period has a time length of Δt, and each time period is sequentially taken as a time period t i . The superscript (1) and subscript N in the time period t i represent the start time mark and the end time mark of the time period t min , respectively.

[0112] In some embodiments, step S100 specifically comprises:

[0113] Step S110, obtaining the instantaneous three-dimensional flow field data at each time t i in the tracking time t1~t N by a direct numerical simulation method, each being uniform flow field data, and the time length of each adjacent two time periods being Δt, t i The instantaneous three-dimensional flow field data at time t min includes x, y, z, u, v, w of all grid points, wherein the flow direction of the flow field along the main flow velocity is defined as the flow direction, the flow direction is defined as the positive direction of the x-axis, the corresponding instantaneous flow velocity is u, the vertical direction perpendicular to the wall surface of the flow field is defined as the positive direction of the y-axis, the instantaneous flow velocity is v, the horizontal direction parallel to the wall surface and perpendicular to the xy plane is defined as the positive direction of the z-axis according to the right-hand rule, and the corresponding instantaneous flow velocity is w. Each yz plane, xz plane and xy plane in the three-dimensional flow field is assigned an index id_x, id_y and id_z, respectively. The minimum and maximum values of the yz plane index are id_x max and id_x min , respectively, the minimum and maximum values of the xz plane index are id_y max and id_y min , respectively, and the minimum and maximum values of the xy plane index are id_z max and id_z min , respectively.In a specific embodiment of the present application, id_x min , id_y min , and id_z min are all taken as 1. For each time t i , the absolute vortex intensity value R, the direction r of Liutex, and the relative vortex intensity value OmegaR of each grid point in the three-dimensional flow field are calculated to obtain the 11-dimensional feature vector [x, y, z, u, v, w, R, r x , r y , r z , and OmegaR] of each grid point, where r x , r y , and r z are the vector components of the direction r of Liutex in the x, y, and z directions, respectively. The absolute vortex intensity vector Liutex and the relative vortex intensity of the three-dimensional flow field, and the calculation methods of the absolute vortex intensity value R, the direction r of Liutex, and the relative vortex intensity value OmegaR of each grid point in the three-dimensional flow field are known, and will not be described here.

[0114] Step S120: Vortex number initialization

[0115] Step S121: According to the characteristic that the relative vortex intensity value OmegaR obtained in step S110 has clear vortex boundaries, all grid points in the flow field at each time t1 to t N are traversed, and the values of OmegaR<θ1 are set to 0 to obtain different sizes of OmegaR clusters in the processed three-dimensional flow field, where each cluster represents a different vortex with clear boundaries, and θ1 is a first threshold value, which is taken as 0.52 in a specific embodiment of the present application.

[0116] Step S122: All OmegaR clusters in the three-dimensional flow field at each time t1 to t N are traversed, and clusters with less than 3 grid points in the x, y, and z directions are considered to be noise points (whether a complete 9-neighborhood is formed is judged), and the values of the noise points are set to 0 to obtain denoised OmegaR.

[0117] Step S123: According to the grid points with a value of 0 in the denoised OmegaR, it is considered that the vortex range has been exceeded at the corresponding positions, and the absolute vortex intensity value R at the corresponding positions is set to 0 to obtain processed R.

[0118] Step S124, for the processed R, each 9-neighborhood extremum point in the yz plane of id_x=1, the xz plane of id_y=1 and the xy plane of id_z=1 is respectively assigned a different vortex number as a reference point for initialization. Considering that some reference points may exhibit 9-neighborhood extremum points in multiple directions, resulting in multiple vortex numbers, at this time, the x-direction vortex sequence number priority is greater than the y-direction vortex number, the y-direction vortex number priority is greater than the z-direction vortex number priority in order, and then the Liutex direction r of all reference points in the yz plane, the xz plane and the xy plane with index number 1 is extracted according to the index number id_x, id_y and id_z, so as to complete the initialization of the t1~t N+1 Initialization of each minimum index number plane at each time.

[0119] It can be understood that since the vortex relative intensity value OmegaR is a parameter for measuring the proportion occupied by the rotational motion part in the plane of the vortex rotation axis, according to its clear vortex boundary characteristics, strong and weak vortices can be captured at the same time, ensuring that weak vortices can also be reconstructed, and at the same time, the R value after processing is used to initialize each minimum index number plane, ensuring the isotropic vortex reconstruction effect in the subsequent.

[0120] Step S130, undirected graph construction

[0121] Traverse and track time t1~t N Each time and the adjacent two planes parallel to each other, for t i The first id1 and the second id2 planes at the time, first determine the 9-neighborhood extremum points of each vortex absolute intensity value R in the first id1 and the second id2 planes; then divide each 9-neighborhood extremum point in the first id1 plane into a reference node V m , and divide each 9-neighborhood extremum point in the second id2 plane into a to-be-matched node, normalize the 11-dimensional feature vectors of each node to [0, 1] respectively to obtain the normalized feature vectors of each node, and take the mth reference node V m as an example, and denote the pth normalized feature of the reference node V m as f m,p :

[0122]

[0123] Where f m,p is the pth feature of the mth reference node in the undirected graph, and when p is 1, 2, …, 11, f m,p corresponds to x m , y m , z m , u m , v m , wm ,R m ,r mx ,r my ,r mz OmegaR m min(f) m,p ), max(f m,p ) are the minimum and maximum values ​​of the p-th feature of the m-th reference node, respectively;

[0124] When the spatial distance is less than the set maximum connection distance d max Reference node V m and the node to be matched V n Constructing an edge E between them mn ,Right now:

[0125]

[0126] Wherein, the maximum connection distance d max The default is 3 grid units in the flow field;

[0127] Edge weights are set based on the consistency of distance and direction. mn :

[0128]

[0129] Where, σ d σ is a distance scale parameter used to control the sensitivity of distance to edge weights. A value that is too small ignores reasonable matches, while a value that is too large reduces local accuracy. θ σ is a directional scale parameter used to control the sensitivity of the directional angle to the edge weight. A value that is too small ignores small angular deviations, while a value that is too large misjudges reasonable matching. In a specific embodiment of this invention, σ... d and σ θ Take values ​​of 0.1 and 0.2 respectively; For r m and r n The larger the cosine value of the angle between them, the more consistent the rotation directions are, and the greater the possibility that they belong to the same vortex tube or vortex core region.

[0130] Thus, we obtain the undirected graph G. id1_id2 Its expression is:

[0131] G id1_id2 =(V id1_id2 E id1_id2 )

[0132] Among them, V id1_id2 For an undirected graph G id1_id2 The set of nodes, E id1_id2 For an undirected graph G id1_id2 The set of edges.

[0133] In some embodiments, step S200 specifically includes the following steps:

[0134] Step S210, GNN acquisition:

[0135] Step S211, Construction of the first training sample set:

[0136] Step S2111, Acquisition of basic data:

[0137] The continuous time interval τ1~τ2 is obtained by direct numerical simulation. K τ at each time point k For instantaneous three-dimensional flow field data, under conditions of unlimited computational resources, K should be much greater than N, and K should be at least twice N. Each yz plane, xz plane, and xy plane in the three-dimensional flow field is assigned an index number. For each time τ... k Following step S100, the 11-dimensional feature vector [x,y,z,u,v,w,R,r] of each grid point is obtained. x ,r y ,r z [OmegaR] and the initialization of the vortex numbers in each minimum index number plane; it should be noted that the continuous time τ1~τ K The spatial dimensions of the three-dimensional flow field, the duration between two adjacent moments, and the index number of each plane are all consistent with step S100.

[0138] Step S2112: For continuous time τ1~τ K τ at each time point k The basic data were obtained using the following methods to obtain the corresponding vortex three-dimensional multi-directional reconstruction results:

[0139] According to τ k At each time step, the current vortex information of the plane with the smallest index number is used, and the vortex is reconstructed in both positive and negative directions in the x, y, and z directions sequentially, with the constraint of matching with the nearest prediction point first. The position of the prediction point is obtained by the constraint calculation of the direction r of Liutex. The current number of vortices is counted, and the current round of vortex 3D multi-directional reconstruction ends. Multiple rounds of vortex 3D multi-directional reconstruction are performed according to the above steps. When the number of vortices converges, τ is completed. k Time-lapse vortex 3D multi-directional reconstruction, preserving τ k The indices of all vortices and their 11-dimensional eigenvectors at time τ are used as τ. k The result of three-dimensional multi-directional reconstruction of the vortex at any given time.

[0140] Furthermore, during the multi-directional reconstruction of the single-wheel vortex in step S2112, firstly based on τ kThe vortex information of each minimum index number plane is recorded, and the positive and negative bidirectional reconstruction of the vortex is performed in the x, y, and z directions in turn, and then the number of vortices in the three-dimensional flow field is counted; when performing positive reconstruction, first, the two adjacent planes are positively matched in turn according to the order of the index number from small to large, until the positive matching of the maximum index number plane and the minimum index number plane is completed, and then the two adjacent planes are negatively matched in turn according to the order of the index number from large to small, until the negative matching of the minimum index number plane and the maximum index number plane is completed; wherein, for the two adjacent planes to be matched,

[0141] For positive matching, 9-neighborhood extreme points in the plane with a smaller index number that have been assigned a vortex number are selected as reference points respectively, the projection positions of each reference point in the plane with a larger index number are predicted respectively by using the positive normalized value of the component of the Liutex direction r, to obtain the corresponding matching points, and the matching points are assigned the same vortex number as the reference points; for 9-neighborhood extreme points in the plane with a larger index number that have not been assigned a vortex number and have a component of the Liutex direction r greater than 0, new vortex numbers are assigned to them;

[0142] For negative matching, each 9-neighborhood extreme point in the plane with a larger index number that has a component of the Liutex direction r less than 0 is selected as a reference point respectively, and new vortex numbers are assigned to the reference points that have not been assigned a vortex number, the projection positions of each reference point in the plane with a smaller index number are predicted respectively by using the negative normalized value of the component of the Liutex direction r, to obtain the corresponding matching points, and the matching points are assigned the same vortex number as the reference points; for 9-neighborhood extreme points in the plane with a smaller index number that have not been assigned a vortex number and have a component of the Liutex direction r less than 0, new vortex numbers are assigned to them.

[0143] More specifically, when step S2112 performs a single round of vortex multi-direction reconstruction, each round performs positive and negative bidirectional reconstruction of the vortex in the x, y, and z directions in turn, and the specific steps are as follows:

[0144] Step S2112a, according to the current vortex information of the first yz plane, the positive and negative bidirectional reconstruction of the vortex in the x direction is performed:

[0145] For the positive matching process: see Figure 2 , for the id x and id x+1 yz planes, each 9-neighborhood extreme point in the id x yz plane that has been assigned a vortex number is selected as a reference point, for each reference point, the component r xNormalized to dx, the projection point of the current reference point on the id_x+1th yz plane is calculated based on dx. This projection point is used as the predicted position. Then, the nearest 9-neighbor extreme points of the predicted position are selected from the set area of ​​the id_x+1th yz plane as the matching points of the current reference point. The distance between the matching point and the reference point is calculated. If it is less than the maximum matching distance MCR, the matching point is assigned the same vortex number as the reference point; otherwise, the reconstruction of the vortex in this direction is stopped. After all reference points in the id_xth yz plane have been traversed, for the id_x+1th yz plane where no vortex number has been assigned and r x For each 9-neighbor extreme point greater than 0, a new vortex number is assigned. This new vortex number does not repeat any existing vortex numbers in any of the current planes. The forward matching of the id_x-th yz-plane with the id_x+1-th yz-plane is then completed. Subsequently, the 9-neighbor extreme points with assigned vortex numbers in the id_x+1-th yz-plane are selected as reference points. The above steps are repeated to perform the forward matching of the id_x+1-th yz-plane with the id_x+2-th yz-plane. This process continues until the id_x-th yz-plane is completed. max -1 and the id_x max After the positive matching of the yz plane, for the id_x-th plane... max Each reference point on the yz plane is positively matched with the first yz plane using the same steps described above. This completes the positive reconstruction of the vortex in the x-direction. The maximum matching distance MCR is calculated using the following formula:

[0146]

[0147] In the formula: α is a coefficient, which generally ranges from 1 to 1.5, and is taken as 1.3 in this embodiment. V N represents the total area of ​​the vortex region (located in the yz plane). yz This represents the number of 9-neighborhood extrema of an independent vortex cross section; it should be noted that the same maximum matching distance (MCR) is used in the x, y, and z directions.

[0148] For the negative matching process: for the id_x... max In a yz plane, select 9 neighborhood extreme points where the component of r in the Liutex direction in the x direction is less than 0, and use each of these as a reference point. Assign new vortex numbers to the reference points that have not yet been assigned vortex numbers. For each reference point, the component r in the Liutex direction in the x direction is... x Normalized to -dx, the current reference point is calculated at the id_x position based on -dx. max The projection point on the -1 yz plane is used as the predicted position, and then the projection point is used from the id_x-th plane. max-1 yz plane, the 9-neighborhood extremum point closest to the predicted position in the set region is selected as the matching point of the current reference point, the distance between the matching point and the reference point is calculated, if it is less than the maximum matching distance MCR, the matching point is assigned the same vortex number as the current reference point, otherwise the reconstruction of the vortex in this direction is stopped, if the matching point already has a vortex number, it needs to be updated to the new reference point vortex number; when all the reference points of the id_x max th yz plane are traversed, the id_x max th yz plane is screened, each 9-neighborhood extremum point with r x less than 0 is taken as a reference point, and a new vortex number is assigned to the reference point that has not been assigned a vortex number in the id_x max th yz plane, the negative matching of the id_x max th yz plane is completed, for each reference point of the id_x max th yz plane, the above steps are repeated to perform negative matching with the id_x max th and the id_x max th yz plane, after the negative matching of the 2nd and the 1st yz planes is completed, for each reference point on the 1st yz plane, the above steps are repeated to perform negative matching with the id_x y th yz plane, thus the vortex negative reconstruction in the x direction is completed.

[0149] Step S2112b, according to the current vortex information of the 1st xz plane and the bidirectional reconstruction results in the x direction, the vortex positive and negative bidirectional reconstruction in the y direction is performed:

[0150] For the positive matching process: for the id_y and id_y+1 xz planes, each 9-neighborhood extremum point in the id_y xz plane that already has a vortex number is taken as a reference point, for each reference point, the 9-neighborhood extremum points of the id_y+1 xz plane are matched, the matching process is the same as the positive matching process in the x direction, that is, the component r ythe 9-neighborhood extremum point with the maximum absolute value of r in the y direction, assign a new vortex number to it, and complete the positive matching of the id_y-th and the id_y+1-th xz planes; then, select each 9-neighborhood extremum point in the id_y+1-th xz plane that has been assigned a vortex number as a reference point, and repeat the above steps to perform the positive matching of the id_y+1-th and the id_y+2-th xz planes. After the positive matching of the id_y max -1-th and the id_y max -th xz planes is completed, perform the positive matching of the id_y max -th xz plane on each reference point according to the above steps, and the positive reconstruction of the vortex in the y direction is completed.

[0151] For the negative matching process: for the id_y max -th xz plane, select each 9-neighborhood extremum point in which the component r y of the Liutex direction r in the y direction is less than 0 as a reference point, and assign a new vortex number to the reference point that has not been assigned a vortex number. For each reference point, match it with the 9-neighborhood extremum points of the id_y max -1-th xz plane, and the matching process is the same as the negative matching process in the x direction, that is, normalize r y to -dy, calculate the projection point of the current reference point on the id_y max -1-th xz plane according to -dy, take the projection point as the predicted position, and then select the 9-neighborhood extremum point closest to the predicted position from the set region of the id_y max -1-th xz plane as the matching point of the current reference point, calculate the distance between the matching point and the reference point, and if the distance is less than the maximum matching distance MCR, assign the same vortex number to the matching point as the reference point, otherwise stop reconstructing the vortex in this direction. max After all the reference points in the id_y max -1-th xz plane are traversed, for each 9-neighborhood extremum point in the id_y y -1-th xz plane that has not been assigned a vortex number and in which r max is less than 0 and has the maximum absolute value, assign a new vortex number to it, and complete the negative matching of the id_y max -th and the id_y max -1-th xz planes; then, select each 9-neighborhood extremum point in the id_y max -1-th xz plane that has been assigned a vortex number as a reference point, and repeat the above steps to perform the negative matching of the id_y max- Two negative matching operations are performed on the xz planes. After completing the negative matching between the second and first xz planes, for each reference point on the first xz plane, the same steps as described above are followed with the id_y-th xz plane. max Negative matching was performed on the xz planes, thus completing the negative reconstruction of the vortex in the y direction;

[0152] Step S2112c: Based on the vortex information of the first xy plane and the bidirectional reconstruction results in the x and y directions, perform bidirectional reconstruction of the positive and negative vortexes in the z direction:

[0153] For the forward matching process: For the id_z-th and id_z+1-th xy-planes, select each of the 9 neighboring extreme points in the id_z-th xy-plane that already has a vortex number as a reference point. For each reference point, match it with the 9 neighboring extreme points in the id_z+1-th xy-plane. The matching process is the same as the forward matching process in the y-direction, that is, the component r of the Liutex direction in the z-direction. z Normalized to dz, the projection point of the current reference point on the (id_z+1)th xy-plane is calculated based on dz. This projection point is used as the predicted position. Then, the nearest 9-neighbor extreme points to the predicted position are selected from the set area of ​​the (id_z+1)th xy-plane as the matching points of the current reference point. The distance between the matching point and the reference point is calculated. If it is less than the maximum matching distance MCR, the matching point is assigned the same vortex number as the reference point; otherwise, the reconstruction of the vortex in this direction is stopped. After all reference points in the (id_z)th xy-plane have been traversed, for those in the (id_z+1)th xy-plane that have not been assigned vortex numbers and r z Nine neighboring extreme points with an absolute value greater than 0 and the maximum value are assigned new vortex numbers, completing the positive matching of the id_z-th xy-plane with the id_z+1-th xy-plane. Then, each of the nine neighboring extreme points with assigned vortex numbers in the id_z+1-th xy-plane is selected as a reference point, and the above steps are repeated to perform the positive matching of the id_z+1-th xy-plane with the id_z+2-th xy-plane. This process continues until the id_z-th xy-plane is completed. max -1 and the id_z max After the positive matching of the xy plane, for the id_z-th plane... max Each reference point on the xy plane is positively matched with the first xy plane using the same steps as described above. Thus, the positive reconstruction of the vortex in the z direction is completed.

[0154] For the negative matching process: for the id_z... max In a plane of xy, filter the components r of the Liutex direction r in the z direction. z Each of the 9 neighboring extreme points less than 0 is taken as a reference point. New vortex numbers are assigned to the reference points that have not yet been assigned vortex numbers. For each reference point, it is compared with the id_z-th vortex.max -1 xy plane, the matching process is the same as the negative matching process in the y direction, that is, r is normalized as -dz, and the current reference point in the id_z z -1 xy plane is calculated according to -dz, and the projection point in the id_z max -1 xy plane, the projection point is taken as the predicted position, and the nearest 9-neighborhood extreme point in the set region of the id_z max -1 xy plane, if it is less than the maximum matching distance MCR, the matching point is assigned the same vortex number as the reference point, otherwise the reconstruction of the vortex in this direction is stopped; when the id_z max -1 xy plane is completed, the id_z max -1 xy plane, and r z -1 xy plane, and the absolute value is the maximum, a new vortex number is assigned to it, and the id_z max -1 xy plane is completed; then the 9-neighborhood extreme points in the id_z max -1 xy plane are screened, each 9-neighborhood extreme point with an assigned vortex number in the id_z max -1 xy plane is repeated, and the id_z max -1 xy plane is completed; then the 9-neighborhood extreme points in the id_z max -2 xy plane, after the negative matching of the 2nd and 1st xy plane is completed, the negative matching of the 1st xy plane is performed according to the above steps and the id_z max -1 xy plane, and the negative reconstruction of the vortex in the z direction is completed, the number of vortices in the current three-dimensional flow field is counted, and the vortex multi-direction reconstruction process at time τ k is completed.

[0155] It can be understood that steps S2112a-S2112c effectively match the vortex axes in three-dimensional directions of the flow field, allowing isolated axis points in the vertical and spanwise directions to start matching new vortices, taking into account the three-dimensional sampling effect, and having better reconstruction effect on isotropic vortices, effectively improving the vortex reconstruction rate; at the same time, the predicted point position is calculated through the vector direction constraint characteristic of Liutex, and the physical constraint condition of preferentially matching the nearest predicted point is set, effectively reducing the phenomenon of matching pseudo-vortex axis points connected by proximity, and the three-dimensional multi-direction reconstruction result of the vortex obtained in step S2112 is used as a real label for subsequent training of GNN.

[0156] In step S2112, the vortex multi-direction reconstruction process at time τ kAt this moment, the vortex multi-direction reconstruction process of steps S2112a-S2112c needs to be repeated at least once, and whether the vortex quantity converges is determined by whether the difference between the vortex quantities counted in the front and back two rounds is less than the second threshold θ2, θ2 is generally a small positive number, and in this embodiment, it is 3. If it does not converge, steps S2112a-S2112c are continuously repeated until the vortex quantity converges, and at this moment τ k At this moment, the vortex three-dimensional reconstruction is completed, and τ k At this moment, the 11-dimensional feature vectors of all the vortexes are saved, and then according to actual needs, interpolation mapping can be performed according to the size of R to achieve the visualization of the vortex structure in the flow field, see Figure 3 .

[0157] Step S2113, first training sample construction:

[0158] According to the vortex three-dimensional multi-direction reconstruction results of K moments obtained in step S2112, the corresponding undirected graphs G are constructed according to step S130 id1_id2 The difference is that Each node in G id1_id2 is a vortex axis point in the corresponding plane in the vortex three-dimensional multi-direction reconstruction result obtained in step S2112; each undirected graph G is taken as a first training sample, all first training samples are used to construct a first training sample set, the samples in the first training sample set are randomly shuffled in sequence to avoid model overfitting to the connection rules of a specific moment or a specific plane sequence in the training process. The samples after random shuffling are divided into multiple batches, and each batch may contain undirected graphs from different moments and different directions to improve the diversity of training data.

[0159] Step S212, GNN construction and training:

[0160] A L=3-layer graph neural network GraphSAGE (Graph Sample and Aggregate) is designed as the basic framework of GNN, and the first training sample set constructed in step S211 is used to train GNN in batches to obtain a trained GNN; for each input first training sample, GNN updates the embedding vectors of all nodes in the input undirected graph, and the update process is as follows:

[0161] h e (l+1) = ReLU(W (l) · MEAN({h g (l) |g∈N(g)}) + B (l) h e (l) )

[0162] Among them, h e (l) and h g (l) For the GNN at layer l, the nodes are V. e and node V g The generated embedding vector, node V e and node V g An undirected graph There are two nodes with an edge in the array; N(g) is the node V. e The neighborhood of W; (l) With B (l) These are the weight matrix and bias vector of the l-th layer of the GNN, respectively; ReLU is the activation function used in the hidden layer of the GNN; MEAN is the mean aggregation function, which calculates the average value of the neighbor features and is used for message passing in the GNN, suitable for capturing the local characteristics of vortex points.

[0163] For each pair of nodes (V) e V g GNN uses its output layer (a fully connected layer) to predict node V. e With node V g Matching tags The prediction process is as follows:

[0164]

[0165] in, Through node V e With node V g The probability of belonging to the same vortex is represented; Sigmold is the activation function used in the output layer of the GNN, which maps the input values ​​to the [0,1] interval, converting the result of the linear transformation into probability values; W out The linear transformation matrix of the weights of the GNN output layer determines the node V. e and V g How do the features of b affect the matching probability? out This is the offset, used to provide an offset for the linear transformation of the matching probability, adjusting the baseline value of the prediction;

[0166] For undirected graphs All nodes V e Predict V using the output layer of GNN e pseudo-matching tags

[0167]

[0168] in, Using node V eThe probability of pseudo-matching points is characterized. Pseudo-matching points refer to vortex axis points in a three-dimensional flow field that meet any of the following conditions: (1) noise points that do not belong to the real vortex structure, such as points where OmegaR < θ1 in step S121, θ1 = 0.52, or vortex axis points where the number of grid points in the OmegaR cluster in the x, y, and z directions is less than 3; (2) points with topological anomalies, where the Liutex direction r differs significantly from that of adjacent points. θ3 is the third threshold, and in this embodiment, θ3≈0.8; (3) Due to proximity, mismatched vortex axis points may be incorrectly matched to other vortex axes due to spatial proximity, thus disrupting the physical consistency of the vortex structure; W pscudo The weight matrix for pseudo-match prediction maps the features of a single node to a one-dimensional scalar; b pscudo The bias scalar is used to adjust the tendency of nodes to be marked as pseudo-matches in the pseudo-match prediction.

[0169] Set the loss function L of GNN GNN :

[0170]

[0171] Among them, L ce The cross-entropy loss function is y. eg Node V is set based on the vortex 3D reconstruction result corresponding to the first training sample. e With node V g True match tag, y eg =1 indicates node V e With node V g Belonging to the same vortex, y eg =0 indicates node V e With node V g Belonging to different vortices; z e Node V is set based on the vortex 3D reconstruction result corresponding to the first training sample. e True and false matching tags, z e =1 indicates node V e For pseudo-matching points, z e =0 indicates node V e λ represents the true matching point; λ is the weight of the pseudo-matching loss, which is set to 0.1 here; μ is the weight of the orientation constraint, which is set to 0.1 here; E is the set of edges of the input undirected graph.

[0172] The GNN is trained using the first training sample set until the maximum number of training iterations is reached or the reconstruction accuracy meets the requirements. Training of the GNN then stops. For each of the first training samples, the GNN obtains a vortex axis prediction set A. GNN_k .

[0173] Understandably, GNNs, based on topological consistency, physical constraints (directional consistency and intensity continuity), supervised learning, and isotropic criteria, rapidly predict vortex axes. Specifically, GNNs take undirected subgraph pairs of adjacent planes as input, capture the global topology through GraphSAGE, predict cross-plane connectivity probabilities, and use the direction term in the loss function. By ensuring that the connections satisfy the consistency of the Liutex direction and the continuity of intensity, while reducing the false matching rate, GNN improves the reconstruction effect of isotropic vortices when processing undirected graphs in the x, y, and z directions respectively.

[0174] Step S220, GNN prediction:

[0175] t i All undirected graphs in the three directions at time t, along with their initialized vortex numbers, are input into the GNN obtained in step S210 in three batches. Each batch inputs all undirected graphs and their initialized vortex numbers in the same direction. Subsequently, the GNN performs positive and negative direction matching on all undirected graphs input in the same batch to obtain t. i The initial set A of vortex axes at time t. GNN_i It includes matching relationships in all directions, specifically:

[0176] For positive matching in the x-direction: starting from id_x in ascending order of plane index numbers. min Initially, for the undirected graph G in the id_x-th and id_x+1-th yz planes input to the GNN... (id_x)_(id_x+1) For the node V in the undirected graph that has been assigned a vortex number m GNN predicts matching node V n If node V m Matching node V n Matching tags Then assign the matching node V n With node V m The same vortex number, θ connect A set probability threshold is used to filter high-confidence matches, ensuring consistency in direction, intensity, and space. To adapt to the complexity of the flow field, θ connect Take 0.7; otherwise, use G. (id_x)_(id_x+1) Unnumbered and r x Assign a new number to nodes with a value greater than 0; update id_x and iterate until the node with the value id_x is reached. max The one with the id_x min Each yz plane completes a positive matching prediction;

[0177] For negative matching in the x-direction: start from id_x in descending order of plane index number. max Begin by filtering r xFor nodes less than 0, input the undirected graph G in the yz plane between the id_x-th and id_x-1-th nodes. (id_x)_(id_x-1) To the GNN, for the node V in the undirected graph that has been assigned a vortex number... m GNN predicts matching node V n If node V m Matching node V n Matching tags Then assign the matching node V n With node V m The same vortex number; otherwise, it is an undirected graph G. (id_x)_(id_x-1) Unnumbered and r x Assign a new number to nodes with a value less than 0; update id_x and iterate until the node with the value less than id_x is reached. min With the id_x max Each yz plane completes negative matching prediction;

[0178] For the positive matching in the y direction: predict the positive matching of each two adjacent xz planes according to the above prediction process for the positive matching of the yz plane;

[0179] For negative matching in the y direction: predict the negative matching of each two adjacent xz planes according to the above prediction process for negative matching in the yz plane;

[0180] For the positive matching in the z direction: predict the positive matching of each two adjacent xy planes according to the above prediction process for the positive matching of the yz plane;

[0181] For negative matching in the z direction: predict the negative matching of each pair of adjacent xy planes according to the above prediction process for negative matching in the yz plane;

[0182] False matching suppression: After completing the above positive and negative matching predictions, discard the false matches. The node is excluded from subsequent vortex axis matching, the matching relationship is updated, and t is obtained. i The initial set A of vortex axes at time t is GNN_i .

[0183] Step S230, Obtaining the RL Model:

[0184] Step S231, Construction of the second training sample set:

[0185] The vortex axis prediction set A output in step S212 will be... GNN_k and with A GNN_k The corresponding GNN has node V in the Lth layer. e The generated embedding vector h e (L) Node V e With node Vg Matching tags and each node V e pseudo-matching tags Together they form a second training sample, and the second training sample set is constructed from all the second training samples.

[0186] Step S232, RL model environment construction:

[0187] In the τ-th step of decision-making for the RL model (corresponding to a state-action-reward interaction), the current node V is... e normalized eigenvector f' e And GNN has node V in layer L. e The generated embedding vector h e (L) The data is concatenated into D+11 dimensional data and used as the state s. τ D represents the dimension of each hidden layer in the GNN, which is taken as 64 in this embodiment, and 11 represents the feature dimension of each node; define action a. τ ={a1,a2,a3,a4,a5,a6,a7}, where a1 and a2 represent positive and negative matching in the x direction, respectively; a3 and a4 represent positive and negative matching in the y direction, respectively; a5 and a6 represent positive and negative matching in the z direction, respectively; and a7 represents terminating the matching and assigning a new vortex number.

[0188] Define reward function r τ :

[0189]

[0190] Among them, R max It is the largest absolute vortex intensity among all the second training samples.

[0191] Step S233, RL Model Design and Training:

[0192] The RL model is defined as a multilayer perceptron (MLP) with L=3 layers, and its input is a 75-dimensional state s. τ The output is a 7-dimensional motion a τ The probability, i.e., in state s τ The algorithm predicts the probabilities of seven possible actions using Proximal Policy Optimization (PPO), with the objective function set as J(θ). RL ):

[0193]

[0194] in, To calculate the expected value of the function; ε τis the discount factor for the step τ, here 0.9, θ RL is the network parameter of the RL model;

[0195] The RL model iteratively optimizes the vortex axis prediction set A GNN_k in the second training sample according to the following steps:

[0196] When the RL model is optimized for the first time, the A GNN_k initialization reference node V e ∈A GNN_k is used; in subsequent optimizations, the output of the last RL model is used to initialize each reference node for the next optimization;

[0197] For each direction (x, y, z): input state s τ , predict action a τ ;

[0198] If a τ is a matching operation, check the matching node V g predicted by the GNN for direction consistency and intensity continuity, and calculate the reward r τ ; if a τ is a termination operation, assign a new vortex number to the current reference node V e being processed; update the features and GNN embedding vectors by switching to the next node, record the plane index and vortex number and update the state s τ , iterate until all nodes complete vortex number assignment, count the number of vortices at the end of this iteration, and enter the next RL optimization;

[0199] If the vortex number change rate of the last 3 RL iterations is less than 1%, stop iteration and output the vortex axis optimization set A k at time τ opt_k , containing the vortex number and 11-dimensional feature vector of each vortex axis point.

[0200] Step S240, the RL model applies:

[0201] Use the trained RL model to perform multiple iterative optimizations on the vortex axis initial set A i at time t GNN_i obtained in step S220 until the vortex number converges, stop iteration and optimization, and output the vortex axis optimization set A i at time t opt_i .

[0202] It can be understood that, due to the biased model architecture static prediction characteristics of the GNN in predicting the vortex axis and the insufficient modeling of complex physical constraints, the RL model is adopted to suppress the false matching in the vortex axis predicted by the GNN based on the direction consistency and intensity continuity criteria, thereby improving the prediction accuracy of the vortex axis.

[0203] In some embodiments, step S300 specifically comprises the following steps:

[0204] Step S310, single-vortex tracking during period t1-t2:

[0205] According to the vortex axis optimization set A at time t1 obtained in step S200 opt_1 , all vortices at the starting time t1 of the period t1-t2 are sequentially tracked as target vortices, specifically:

[0206] Step S311, based on the vortex axis optimization set A at time t1 opt_1 , the vortex absolute intensity values R of all vortex axis points on the current target vortex are sorted from large to small, and the top B vortex axis points are taken as absolute rotation intensity dominant points, and are recorded as tracking points. The 11-dimensional feature vector of each tracking point is recorded. B is adjusted according to the observation needs (such as observation accuracy), and generally recommended to be greater than 5;

[0207] Step S312, predicted position P of each tracking point at time t2 predicted Calculation and search range setting:

[0208] The predicted position P of each tracking point at time t2 is calculated according to the following formula: predicted

[0209] P predicted = P current + V·Δt

[0210] In the formula, P current =(x, y, z) is the position of the tracking point at time t1, V=(u, v, w) is the velocity of the tracking point at time t1, and Δt is the time length of the adjacent two times, Δt=t2-t1;

[0211] For each tracking point, a respective cuboid search range is defined, which is η times the displacement of the corresponding tracking point:

[0212] X range =[X predicted -η·|u·Δt|, X predicted +η·|u·Δt|]

[0213] Y range =[Y predicted -η·|v·Δt|, Y predicted ​+η·|v·Δt|]

[0214] Z range =[Z predicted -η·|w·Δt|,Z predicted +η·|w·Δt|]

[0215] In the formula: X range Y range and Z range These represent the search ranges of a given tracking point in the x, y, and z directions, respectively; X predicted Y predicted and Z predicted These are the predicted positions of a certain tracking point in the x, y, and z directions at time t2, respectively; η is a constant, generally ranging from (0, 0.5], and is taken as 0.3 in this embodiment;

[0216] Step S313: Optimize the vortex axis set A based on time t2. opt_2 Within the cuboid search range corresponding to each tracking point, vortex axis points are searched. If the ratio of the number of vortex axis points B' with the same vortex number to B is greater than the fourth threshold θ4 (θ4 is generally taken as 0.6), then the vortex is considered to be the tracked vortex, i.e., the tracking is successful, and the same time tag is transmitted, i.e., the time tag of the vortex is marked as t1. Otherwise, it is considered that the vortex has dissipated at time t2. After all vortices at time t1 are tracked in sequence, the vortices at time t2 that are not marked with time tags are marked as t2, and it is considered that the vortex originated at time t2. Thus, the single vortex tracking for the time period t1 to t2 is completed.

[0217] Step S320: Following steps S311 to S313, process the subsequent time periods t2 to t2,...,t i ~t i+1 ,...,t N-1 ~t N Perform single-vortex tracking sequentially;

[0218] Step S330, statistical tracking time t1~t N Each vortex with the same vortex number that has been successfully tracked is considered a separate vortex tracking subsequence. The tracking time t1 to t2 is composed of all these vortex tracking subsequences. N Vortex tracking sequence The superscript (1) and subscript N in the text represent respectively The start time marker and the end time marker; It contains multiple vortex tracking subsequences with different start times and different time lengths.

[0219] See Figure 4A tracking schematic diagram obtained by using step S300 to track a single vortex across time and space.

[0220] It can be understood that step S300 realizes tracking of a single vortex across time by extracting vortex axis points with dominant absolute rotational intensity and according to the position and speed of the predicted tracking point, so that the change in structure of the single vortex when evolving over time in the flow field can be intuitively observed.

[0221] The vortex reconstruction and tracking device provided in the second aspect of the present application comprises:

[0222] The first module is configured to obtain instantaneous three-dimensional flow field data at each time t N of the time period t i , assign index numbers to each plane parallel to the x, y and z directions, calculate the vortex absolute intensity value R, the direction r of the vortex absolute intensity vector Liutex and the vortex relative intensity value OmegaR of each grid point in the three-dimensional flow field for each time t i , and obtain the feature vector of each grid point in combination with the position and instantaneous flow rate of the grid point, and initialize the vortex numbering in each minimum index number plane based on the feature vector of each grid point; construct an undirected graph G id1_id2 based on the feature vectors of the 9-neighborhood extreme points of each vortex absolute intensity value R in the adjacent two planes at the same time and parallel to each other, and the index numbers of the two adjacent planes used when constructing the undirected graph are represented by the subscripts id1 and id2 respectively.

[0223] The second module is configured to input all undirected graphs at time t i and the initial vortex numbering into a pre-trained graph neural network, the graph neural network predicts the matching relationship of the vortex axis based on the topological consistency, supervised learning and isotropic criterion, and obtains an initial set of vortex axes A i at time t GNN_i ; input A GNN_i into a pre-trained reinforcement learning model, the reinforcement learning model suppresses the pseudo-matching in A GNN_i based on the directional consistency and intensity continuity criterion, and obtains an optimized set of vortex axes A i at time t opt_i ; A GNN_i and A opt_i record the numbering of each vortex and the feature vector of each vortex at different vortex axis points respectively.

[0224] The third module is configured to start from the time period t1-t2, sequentially track each time period t i -t i+1 in chronological order, until t N-1 -t Na time period, to obtain a vortex tracking sequence t1~t N a vortex tracking sequence t1~t a single-vortex tracking process for a time period t i ~t i+1 includes:

[0225] all the vortices at time t i are sequentially taken as target vortices, and a vortex axis point with a dominant vortex absolute intensity value R is extracted based on information of the target vortex in A opt_i and taken as a tracking point, and a position and a speed of the tracking point at time t i+1 are predicted, and it is judged whether the target vortex is dissipated at time t i+1 , if not, it is determined that the target vortex is successfully tracked, and an origin time of the target vortex is marked as time t i+1 .

[0226] vortices with the same vortex number and successfully tracked in a tracking time t1~t N are respectively taken as a vortex tracking sub-sequence, and all the vortex tracking sub-sequences constitute a vortex tracking sequence t1~t N .

[0227] It should be noted that the vortex reconstruction and tracking method of the foregoing embodiments is also applicable to the vortex reconstruction and tracking device of the present embodiment, and will not be repeated here.

[0228] In order to implement the foregoing embodiments, the present embodiment also proposes a computer readable storage medium having a computer program stored thereon, the program being executed by a processor to execute the vortex reconstruction and tracking method of the foregoing embodiments.

[0229] Reference will now be made to Figure 5 , which shows a structural schematic diagram of an electronic device suitable for implementing the embodiments of the present disclosure. It should be noted that the electronic device in the embodiments of the present disclosure can include, but is not limited to, mobile terminals such as mobile phones, notebook computers, digital broadcast receivers, PDAs (personal digital assistants), PADs (tablets), PMPs (portable multimedia players), vehicle-mounted terminals (such as vehicle-mounted navigation terminals), and the like, and fixed terminals such as digital TVs, desktop computers, servers, and the like. Figure 5 The electronic device shown is only an example, and should not impose any limitation on the functions and use range of the embodiments of the present disclosure.

[0230] As Figure 5As shown, the electronic device can include a processing device (e.g., a central processing unit, a graphics processing unit, etc.) 101 that can perform various appropriate actions and processes according to programs stored in a read-only memory (ROM) 102 or loaded into a random access memory (RAM) 103 from a storage device 108. Various programs and data required for operation of the electronic device are also stored in the RAM 103. The processing device 101, the ROM 102, and the RAM 103 are connected to each other through a bus 104. An input / output (I / O) interface 105 is also connected to the bus 104.

[0231] In general, the following devices can be connected to the I / O interface 105: input devices 106 including, for example, a touch screen, a touch pad, a keyboard, a mouse, a camera, a microphone, etc.; output devices 107 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; storage devices 108 including, for example, a magnetic tape, a hard disk, etc.; and communication devices 109. The communication devices 109 can allow the electronic device to communicate wirelessly or wired with other devices to exchange data. Although Figure 5 The electronic device is shown with various devices, but it is understood that all of the shown devices are not required to be implemented or present. More or less devices can alternatively be implemented or present.

[0232] In particular, according to embodiments of the present disclosure, the processes described above with reference to the flowcharts can be implemented as a computer software program. For example, the present embodiments include a computer program product comprising a computer program carried on a computer readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network through the communication devices 109, or installed from the storage devices 108, or installed from the ROM 102. When the computer program is executed by the processing device 101, the above-mentioned functions defined in the methods of the present disclosure embodiments are performed.

[0233] It is noted that the aforementioned computer-readable medium of the present disclosure can be a computer-readable signal medium or a computer-readable storage medium or any combination thereof. The computer-readable storage medium can be, for example and without limitation, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of the computer-readable storage medium can include, but are not limited to, an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the present disclosure, the computer-readable storage medium can be any tangible medium that contains or stores a program used by or in connection with an instruction execution system, apparatus, or device. In the present disclosure, the computer-readable signal medium can include a data signal propagated in baseband or propagated as a carrier wave in a propagated data signal, in which the computer-readable program code is contained. Such a propagated data signal can take a variety of forms, including but not limited to electro-magnetic, optical, or any suitable combination thereof. The computer-readable signal medium can also be any computer-readable medium that is not a storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to wire, cable, RF, etc., or any suitable combination of the foregoing.

[0234] The aforementioned computer-readable medium can be contained in the aforementioned electronic device; or can exist separately from the electronic device.

[0235] The aforementioned computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the aforementioned vortex reconstruction and tracking method.

[0236] Computer program code for carrying out operations of the present disclosure can be written in any one or more programming languages or combinations of languages including object or visual programming languages such as Java, Smalltalk, C++, Python, conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0237] In the description of the specification, the description of the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Also, the specific features, structures, materials or characteristics described can be combined in any appropriate manner in any one or more embodiments or examples. In addition, the person skilled in the art can combine and combine the different embodiments or examples described in the specification and the features of the different embodiments or examples, without contradiction.

[0238] In addition, the terms "first", "second", etc. are used only for the purpose of description and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, the features defined with "first", "second" can explicitly or implicitly include at least one of the features. In the description of the present application, the meaning of "a plurality of" is at least two, for example, two, three, etc., unless otherwise specifically limited.

[0239] Any process or method descriptions or descriptions of the flow diagrams in the specification or otherwise described herein can be understood as representing code modules, segments, or portions of code which include one or more executable instructions for implementing specific logic functions (or steps) in the process, and the various embodiments of the application include additional implementations in which the order of execution or the specific logic functions (or steps) can be changed, including according to the functionality involved, without departing from the scope of the embodiments of the application. It should be understood that the embodiments of the application can be practiced with additional combinations of hardware and software, and that the embodiments of the application can be implemented with hardware equivalent to software, with software equivalent to hardware, or each independently with hardware or software.

[0240] The logic and / or steps represented in the flowcharts and / or described herein, for example, can be considered as a sequence of instructions to implement logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, apparatus, or device, such as a computer-based system, processor- based system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For purposes of this specification, a "computer-readable medium" can be any apparatus that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. The computer-readable medium can be a computer- readable storage medium or a computer-readable signal medium. The computer- readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium include the following: an electrical connection having one or more wires (electrical connections), a portable computer diskette (a magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium can even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, for example, via optical scanning of the paper or other medium, then compiled, interpreted, or otherwise processed in a suitable manner, if necessary, and stored in a computer memory.

[0241] It should be understood that aspects of the application can be implemented in hardware, software, firmware or combinations thereof. In the above embodiments, the various steps or methods can be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, and in another embodiment, any of the following technologies, known in the art, or their combinations can be used: discrete logic circuitry having logic gates for implementing logic functions on data signals, application specific integrated circuits having appropriate combinational logic gates, programmable gate arrays (PGA), field programmable gate arrays (FPGA), and the like.

[0242] Those skilled in the art can understand that all or part of the steps carried out by the above-mentioned embodiment methods can be completed by programs instructing related hardware, and the developed programs can be stored in a computer-readable storage medium. When the program is executed, it includes one of the steps of the method embodiment or a combination thereof.

[0243] In addition, each of the functional units in the various embodiments of the present application can be integrated in one processing module, or each of the units can be physically present separately, or two or more units can be integrated in one module. The integrated module can be implemented in the form of hardware or in the form of a software functional module. When the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it can also be stored in a computer readable storage medium.

[0244] The storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above embodiments within the scope of the present application.

Claims

1. A method of vortex reconstruction and tracking, the method comprising: The method comprises the following steps: Step S100, acquiring tracking time t1~t N at each moment t i Instantaneous three-dimensional flow field data, respectively give index number to each plane parallel to x, y, z direction, for each moment t i , calculate the vortex absolute intensity value R of each grid point in three-dimensional flow field, the direction r of vortex absolute intensity vector Liutex and the vortex relative intensity value OmegaR, and get the feature vector of each grid point combined with the position and instantaneous flow rate of the grid point, based on the feature vector of each grid point, complete the initialization of vortex number in each minimum index number plane; Based on the feature vectors of the 9-neighborhood extreme points of the vortex absolute intensity value R in the adjacent two planes at the same moment and parallel to each other, an undirected graph G id1_id2 , the subscripts id1 and id2 respectively represent the index numbers of the two adjacent planes used when constructing the undirected graph; Step S200, t i The graph neural network at time t is pre-trained by inputting all undirected graphs and the initial vortex number into the graph. The graph neural network predicts the matching relationship of the vortex axes based on topological consistency, supervised learning, and isotropic criteria, thus obtaining t. i The initial set A of vortex axes at time t. GNN_i ; to A GNN_i In the pre-trained reinforcement learning model, the reinforcement learning model applies A based on the principles of orientation consistency and intensity continuity. GNN_i Suppressing pseudo-matches in the data yields t. i Optimization set A of vortex axis at time moment opt_i A GNN_i and A opt_i Each vortex is recorded with its number and its characteristic vector at different vortex axis points. Step S300, starting from time period t i ~t i+1 , each time period t N-1 ~t N is sequentially tracked in time order until t N ~t i , to obtain a vortex tracking sequence of time t i+1 ~t i . The single-vortex tracking process for time period t i ~t i+1 includes: Traverse t i All vortices at time t are sequentially taken as the target vortex, based on A. opt_i Information about the target vortex is used to extract the vortex axis point where the absolute intensity value R of the vortex is dominant and use it as the tracking point. This information is then used to track the target vortex. i+1 The position and velocity of the tracking point are constantly monitored to predict and determine the target vortex at time t. i+1 If the time interval does not dissipate, the target vortex is considered successfully tracked, and the origin time of the target vortex is marked as t. i+1 time; Statistical tracking time t1~t N Each vortex with the same vortex number and successfully tracked is taken as a vortex tracking sub-sequence, and all vortex tracking sub-sequences constitute a vortex tracking sequence T N of tracking time t1~t N (1) .

2. The vortex reconstruction and tracking method of claim 1, wherein, In step S100, the characteristic vector of each grid point is used to initialize the vortex number in each minimum index number plane, comprising: Traverse tracking time t1~t N All grid points in the three-dimensional flow field at each time, OmegaR<θ1 value to 0, get the different size of the OmegaR cluster in the processed three-dimensional flow field, each cluster represents a different clear boundary vortex, θ1 is the first threshold value; Traverse tracking time t1~t N All OmegaR clusters in the three-dimensional flow field at each time are filtered, and clusters with less than 3 grid points in the x, y, and z directions are considered as noise points, and their values are set to 0 to obtain the denoised OmegaR. According to the grid point with the value of 0 in the denoised OmegaR, the absolute intensity value R of the corresponding position of the vortex is set to 0, and a processed R is obtained; For the processed R, different vortex numbers are respectively assigned to each 9-neighborhood extreme point in each minimum index number plane as a reference point. When the reference point is a 9-neighborhood extreme point in multiple directions, the vortex number in the x direction is selected as the priority, followed by the vortex number in the y direction and the vortex number in the z direction. Then, according to the direction r of the Liutex of all reference points in each minimum index number plane, the initialization of the vortex number in each minimum index number plane is completed.

3. The vortex reconstruction and tracking method of claim 1, wherein, In step S100, the undirected graph G id1_id2 The construction step comprises: Traverse tracking time t1~t N Each time and parallel to each other, the adjacent two planes, for t i The first id1 and the second id2 plane at the time, first determine the 9-neighborhood extremum point of each vortex absolute intensity value R in the first id1 and the second id2 plane; then each 9-neighborhood extremum point in the first id1 plane is divided into a reference node V m , each 9-neighborhood extremum point in the second id2 plane is taken as a node to be matched, and the feature vector of each node is normalized to [0, 1] to obtain the normalized feature vector of each node; When the spatial distance is less than the set maximum connection distance d max Reference node V m and the node to be matched V n Constructing an edge E between them mn ; Setting edge weight w based on distance and direction consistency mn : where σ d is a distance scale parameter used to control the sensitivity of the edge weight to the distance; σ θ is a direction scale parameter used to control the sensitivity of the edge weight to the direction angle; is the angle between the Liutex direction r m of the reference node V m and the Liutex direction r n of the node to be matched V n , r mx , r my , r mz are the three-dimensional vector components of r m , r nx , r ny , r nz are the three-dimensional vector components of r n ; According to the set nodes and edges, an undirected graph G is obtained id1_id2 : G id1_id2 = (V id1_id2 , E id1_id2 ) wherein V id1_id2 is a set of nodes of an undirected graph G id1_id2 , E id1_id2 is a set of edges of the undirected graph G id1_id2 .

4. The vortex reconstruction and tracking method of claim 3, wherein, The training process of the graph neural network comprises: Step S211, first training sample set construction: Step S2111, acquiring continuous time τ1~τ K of each moment τ k in the three-dimensional flow field, assigning the same index number to each plane parallel to the x, y, z direction in the three-dimensional flow field as the corresponding plane in step S100, calculating the vortex absolute intensity value R, the direction r of the vortex absolute intensity vector Liutex, and the vortex relative intensity value OmegaR of each grid point in the three-dimensional flow field for each moment τ k , and obtaining the characteristic vector of each grid point in combination with the position and instantaneous flow rate of the grid point, and completing the initialization of the vortex number in each minimum index number plane based on the characteristic vector of each grid point. Step S2112, for each time τ K in the continuous time τ1~τ k , the following method is used to obtain the corresponding vortex three-dimensional multi-direction reconstruction result: According to τ k The current vortex information of each minimum index number plane at the moment is matched with the nearest prediction point as a constraint condition, and the positive and negative bidirectional reconstruction of the vortex is carried out in the x, y and z directions in turn, wherein the position of the prediction point is calculated through the constraint of the direction r of Liutex, the number of current vortices is counted, the current round of three-dimensional multi-directional reconstruction of vortices is ended, and the multi-round three-dimensional multi-directional reconstruction of vortices is carried out according to the above steps, and when the number of vortices converges, τ k The three-dimensional multi-directional reconstruction of vortices at the moment is completed, and τ k The number and characteristic vector of all vortices at the moment are saved as τ k The three-dimensional multi-directional reconstruction result of vortices at the moment; Step S2113, according to the vortex three-dimensional multi-direction reconstruction results of the K time instants obtained in step S2112, respectively constructing an undirected graph based on the feature vectors of the vortex axis points in the same time instant and adjacent two planes parallel to each other Constructing each undirected graph Respectively as a first training sample, constructing a first training sample set by using all the first training samples Step S212, graph neural network construction and training: adopting a L-layer graph neural network, inputting the first training sample into the graph neural network to obtain a corresponding vortex axis prediction set A GNN_k wherein the embedding vectors of all nodes in the input first training sample are updated by using the graph neural network, and the updating process is as follows: h e (l+1) = ReLU(W (l) · MEAN({h g (l) | g e N(g)} ) + B (l) h e (l) ) wherein h e (l) and h g (l) are embedding vectors generated by the graph neural network at the l-th layer for node V e and node V g , respectively; V e and V g are two nodes in the undirected graph G ; N(g) is the neighborhood of node V e ; W (l) and B (l) are the weight matrix and bias vector of the l-th layer of the graph neural network, respectively; ReLU is the activation function adopted by the hidden layer of the graph neural network; and MEAN is the mean aggregation function. For each pair of nodes (V e ,V g ), the graph neural network predicts a matching label e for the pair of nodes (V g ,V e ) using its output layer. The prediction process is as follows: wherein, by the node V e with the node V g characterized by the probability of belonging to the same vortex; Sigmoid is the activation function adopted by the output layer of the graph neural network; W out is the weight linear transformation matrix of the output layer of the graph neural network; b out is the offset; For undirected graphs all nodes V e , using the output layer of the graph neural network to predict the pseudo matching label for V e ​ wherein, adopting a node V e is a probability of a pseudo match point; W pscudo is a weight matrix for pseudo match prediction; b pscudo is a bias scalar for pseudo match prediction; Setting a loss function L of the graph neural network GNN : Among them, L ce The cross-entropy loss function is y. eg Node V is set based on the vortex 3D reconstruction result corresponding to the first training sample. e With node V g True match tags; z e Node V is set based on the vortex 3D reconstruction result corresponding to the first training sample. e The true and false matching labels are λ, the false matching loss weights are μ, the orientation constraint weights are E, and E is the set of edges of the input undirected graph. For node V e The Liutex direction r e and node V g The Liutex direction r g The angle between them.

5. The vortex reconstruction and tracking method of claim 4, wherein, In step S2112, when performing single-round vortex multi-direction reconstruction, first, according to τ k The vortex information of each minimum index number plane at the moment is used to perform positive and negative two-way reconstruction of the vortex in the x, y and z directions in sequence, and then the number of vortexes in the three-dimensional flow field is counted. When performing positive reconstruction, first, the adjacent two planes are positively matched in sequence according to the order of the index numbers from small to large, until the positive matching of the maximum index number plane and the minimum index number plane is completed, and then the adjacent two planes are negatively matched in sequence according to the order of the index numbers from large to small, until the negative matching of the minimum index number plane and the maximum index number plane is completed. For the adjacent two planes to be matched, For forward matching, 9-neighborhood extreme points that have been assigned vortex numbers are selected from the plane with a smaller index number as reference points. The forward normalized value of the component of the Liutex direction r is used to predict the projection position of each reference point in the plane with a larger index number, to obtain the corresponding matching point, and the matching point is assigned the same vortex number as the reference point. For 9-neighborhood extreme points in the plane with a larger index number that have not been assigned a vortex number and have a component of the Liutex direction r greater than 0, a new vortex number is assigned. For negative matching, each 9-neighborhood extreme point with a component of the Liutex direction r less than 0 is selected from the plane with a larger index number as a reference point. A new vortex number is assigned to reference points that have not been assigned a vortex number. The negative normalized value of the component of the Liutex direction r is used to predict the projection position of each reference point in the plane with a smaller index number, to obtain the corresponding matching point, and the matching point is assigned the same vortex number as the reference point. For 9-neighborhood extreme points in the plane with a smaller index number that have not been assigned a vortex number and have a component of the Liutex direction r less than 0, a new vortex number is assigned.

6. The vortex reconstruction and tracking method of claim 4, wherein, In step S200, the graph neural network predicts the matching relationship of the vortex axis, comprising: The t i All undirected graphs in three directions at the time and the initialized vortex number are input into the graph neural network in three batches, all undirected graphs in the same direction and the initialized vortex number are input in each batch, then the graph neural network performs positive and negative direction matching on all undirected graphs input in the same batch, and obtains the vortex axis initial set A i at the t GNN_i time, which contains the matching relationship of each direction, specifically: For positive matching in the x-direction: starting from the yz plane with the smallest index number, matching is performed in ascending order of plane index numbers, for the undirected graph G of the input graph neural network between the id_x-th and id_x+1-th yz planes. (id_x)_(id_x+1) For the node V in the undirected graph that has been assigned a vortex number m The graph neural network predicts matching nodes V n If node V m Matching node V n Matching tags Then assign the matching node V n With node V m The same vortex number, θ connect The set probability threshold is used; otherwise, it is G. (id_x)_(id_x+1) The unnumbered component r of the Liutex direction in the x-direction. x Nodes with a value greater than 0 are assigned a new number; id_x is updated and iterated until the yz plane with the largest index number and the yz plane with the smallest index number complete a positive matching prediction; For negative matching in the x-direction: starting from the yz plane with the largest index number, filter r in descending order of plane index numbers. x For nodes less than 0, input the undirected graph G in the yz plane between the id_x-th and id_x-1-th nodes. (id_x)_(id_x-1) Regarding the graph neural network, for the node V in the undirected graph that has been assigned a vortex number... m The graph neural network predicts matching nodes V n If node V m Matching node V n Matching tags Then assign the matching node V n With node V m The same vortex number; otherwise, it is an undirected graph G. (id_x)_(id_x-1) Unnumbered and r x Nodes with a value less than 0 are assigned a new number; id_x is updated and iterated until the yz plane with the smallest index number and the yz plane with the largest index number complete a negative matching prediction; The matching process in the x direction is used to predict the positive and negative matching of the y direction and the z direction in sequence; Finally, the nodes with pseudo-matching labels greater than a set threshold are removed, the matching relationship is updated, and t i the initial set of vortex axes A at the time t GNN_i .

7. The vortex reconstruction and tracking method of claim 4, wherein, In step S200, the training process of the reinforcement learning model comprises: Step S231, second training sample set construction: An axis of vortex set A is obtained from step S212 GNN_k , and the A GNN_k Corresponding graph neural network at the Lth layer is node V e The generated embedding vector h e (L) , node V e The matching label of node V g And the pseudo matching label of each node V e Together as a second training sample, all second training samples are used to build a second training sample set;​​ Step S232, RL model environment construction: In the τth step of making a decision for the reinforcement learning model, node V... e normalized eigenvector f' e The graph neural network has node V in layer L. e The generated embedding vector h e (L) splicing to form state s τ Define action a τ ={a1,a2,a3,a4,a5,a6,a7}a1 and a2 represent positive and negative matching in the x direction, respectively; a3 and a4 represent positive and negative matching in the y direction, respectively; a5 and a6 represent positive and negative matching in the z direction, respectively; and a7 represents terminating the matching and assigning a new vortex number. Defining the reward function r τ : wherein R max is the maximum absolute vorticity strength among all second training samples; R e and R g are the absolute vorticity strength values of node V e and node V g respectively. Step S233, reinforcement learning model design and training: The reinforcement learning model is defined as a multi-layer perceptron of L layers, with input state s τ , and output probability of 7-dimensional action a τ . The reinforcement learning model uses a proximal policy optimization algorithm, and sets the objective function as J(θ RL ). wherein, is a function of expectation; ε τ is a discount factor at step τ, θ RL is a network parameter of the reinforcement learning model; The reinforcement learning model predicts a set of vortex axis candidates A for a second training sample according to the following steps GNN_k Iterative optimization is performed: The reinforcement learning model uses A GNN_k Initialize the reference nodes V e ∈A GNN_k The output of the last reinforcement learning model is used to initialize each reference node for the next optimization during subsequent optimization. For each direction x, y, z: input state s τ , predicted action a τ ; If a τ To perform the matching operation, the direction consistency and intensity continuity check the matching nodes V g predicted by the graph neural network, and calculate the reward r τ ; if a τ for the termination operation, assign a new vortex number to the reference node V e currently processed; update the feature vector and graph neural network embedding vector by switching to the next node, record the index number and vortex number of the plane and update the state s τ , iterate until all nodes complete vortex number assignment, count the number of vortexes at the end of this iteration, and enter the next reinforcement learning optimization; When the number of vortices obtained by successive reinforcement learning iterations stabilizes, iteration is stopped, and τ is output k The optimized set A of vortex axes at the moment opt_k .

8. The vortex reconstruction and tracking method of claim 4, wherein, Step S300 specifically comprises: Step S310, single-vortex tracking in the time period t1-t2: The vortex axis optimization set A at time t1 obtained according to step S200 opt_1 All the vortexes at time t1 in the time period t1-t2 are sequentially tracked as target vortexes, specifically: Step S311, optimizing the vortex axis set A based on the t1 moment opt_1 The vortex absolute intensity values R of all vortex axis points on the current target vortex are sorted from large to small, the first B vortex axis points are taken as the absolute rotation intensity dominant points, and are recorded as tracking points, and the feature vectors of the tracking points are recorded. Step S312, the predicted position P of each tracking point at t2 is calculated according to the following formula predicted : P predicted = P current + V · Δt In the formula, P current = (x, y, z) is the position of the tracking point at time t1, V = (u, v, w) is the velocity of the tracking point at time t1, and Δt is the time length of the adjacent two times. For each tracking point, a corresponding cuboid search range is defined, and the displacement of the corresponding tracking point is multiplied by η: X range = [X predicted - η · |u · Δt|, X predicted + η · |u · Δt|] Y range = [Y predicted - η · |v · Δt|, Y predicted + η · |v · Δt|] Z range = [Z predicted - η · | w · Δt |, Z predicted + η · | w · Δt | ] wherein: X range , Y range and Z range are the search ranges of a certain tracking point in the x, y, z directions, respectively; X predicted , Y predicted and Z predicted are the predicted positions of the certain tracking point in the x, y, z directions at t2, respectively; Step S313, optimizing the vortex axis line set A based on the time t2 opt_2 In the rectangular search range corresponding to each tracking point, search for vortex axis points, if the ratio of the number B' of vortex axis points with the same vortex number searched to B is greater than the fourth threshold θ4, it is considered that the vortex is a successfully tracked vortex, the time label of the vortex is marked as t1, otherwise it is considered that the vortex has dissipated at the time t2. After tracking all the vortexes at the time t1, mark the vortexes at the time t2 which have not been marked as t2, and consider that the vortex originates from the time t2. Thus, the single vortex tracking of the time period t1-t2 is completed. Step S320, the subsequent each time period t2~t2,..., t i ~t i+1 ,...,t N-1 ~t N Single vortex tracking is sequentially performed; Step S330, counting the tracking time t1-t N Each vortex with the same vortex number and successfully tracked is taken as a vortex tracking sub-sequence, and all vortex tracking sub-sequences form a vortex tracking sequence with the tracking time t1-t N of the vortex tracking sequence 9. A vortex reconstruction and tracking device, characterized by, The computer readable storage medium stores computer instructions for executing the vortex reconstruction and tracking method of any one of claims 1-8. The first module is configured to acquire tracking time t1-t N The instantaneous three-dimensional flow field data at each time t i Each plane parallel to the x, y, z direction is assigned an index number, and the absolute strength value R of each grid point in the three-dimensional flow field, the direction r of the absolute strength vector Liutex of each grid point, and the relative strength value OmegaR of each grid point are calculated for each time t i , and the characteristic vector of each grid point is obtained by combining the position and instantaneous flow rate of the grid point. The initialization of the vortex number in each minimum index number plane is completed based on the characteristic vector of each grid point. A directed graph G id1_id2 is constructed based on the characteristic vectors of the 9-neighborhood extreme points of the absolute strength value R of each vortex in two adjacent planes at the same time and parallel to each other, and the subscripts id1 and id2 represent the index numbers of the two adjacent planes used when constructing the directed graph. a second module configured to input all the undirected graphs at time t i and the initial vortex number into a pre-trained graph neural network, which predicts the matching relationship of vortex axes based on topological consistency, supervised learning and isotropic criteria, to obtain an initial set of vortex axes A i at time t GNN_i ; input A GNN_i into a pre-trained reinforcement learning model, which suppresses the false matches in A GNN_i based on directional consistency and intensity continuity criteria, to obtain an optimized set of vortex axes A i at time t opt_i ; A GNN_i and A opt_i record the number of each vortex and its feature vector at different vortex axis points, respectively; The third module is configured to sequentially track each time period t i ~t i+1 from the time period t1~t2 in time order until t N-1 ~t N , and obtain a vortex tracking sequence of the time period t1~t N . The single-vortex tracking process for the time period t i ~t i+1 includes: Traverse t i All vortices at time t are sequentially taken as the target vortex, based on A. opt_i Information about the target vortex is used to extract the vortex axis point where the absolute intensity value R of the vortex is dominant and use it as the tracking point. This information is then used to track the target vortex. i+1 The position and velocity of the tracking point are constantly monitored to predict and determine the target vortex at time t. i+1 If the time interval does not dissipate, the target vortex is considered successfully tracked, and the origin time of the target vortex is marked as t. i+1 time; Statistical tracking time t1~t N Each vortex with the same vortex number and successfully tracked is taken as a vortex tracking sub-sequence, and all vortex tracking sub-sequences constitute a vortex tracking sequence of tracking time t1~t N The vortex tracking sequence of tracking time t1~t 10. A computer-readable storage medium, characterized in that, The computer readable storage medium stores computer instructions for executing the vortex reconstruction and tracking method of any one of claims 1-8.

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