A transport trajectory method based on flow field smoothness

Abstract

This invention discloses a transmission trajectory method based on flow field smoothness. The method acquires wind field grid data of the target area, uses Gaussian smoothing to filter out high-frequency noise while preserving macroscopic flow characteristics, and improves the signal-to-noise ratio. Then, neighboring points are selected centered on the initial point, and a comprehensive weight is calculated using the inverse power of spatial distance and cosine similarity, thus doubly constraining the spatial proximity and wind direction consistency of neighboring points. The trajectory point position is dynamically predicted based on the weighted average wind speed vector of neighboring points, and spline interpolation is used to force the trajectory to be continuous and differentiable, eliminating abrupt changes at discrete points and generating a smooth and coherent transmission path. This method, through flow field smoothing, weight coupling, and dynamic iteration mechanisms, significantly improves the physical rationality and anti-interference capability of trajectory simulation, and is particularly suitable for the accurate prediction of large-scale cross-regional pollutant transport, providing reliable technical support for regional joint prevention and control and pollution control.

Description

Technical Field

[0001] This invention relates to the field of atmospheric pollutant diffusion field simulation technology, and in particular to a transport trajectory method based on flow field smoothness. Background Technology

[0002] With the intensification of regional air pollution problems, cross-regional joint prevention and control urgently requires accurate pollutant transport trajectory simulation technology as support. Traditional methods (such as Gaussian diffusion models and Lagrange particle tracking) rely on simplified meteorological model assumptions, making it difficult to fully capture the complex spatiotemporal changes of large-scale flow fields. Especially in scenarios of long-distance transport and meteorological abrupt changes such as frontal passage, trajectory prediction errors are easily caused by local turbulence or noise interference, affecting the accuracy of assessing the cross-regional impact of external pollutants. In addition, although machine learning-based prediction methods can handle high-dimensional data, they lack explicit modeling of fluid dynamics laws, resulting in insufficient physical rationality and failing to meet the needs of scientific decision-making. The limitations of existing technologies mean that the simulation of pollutant transport paths under complex meteorological conditions suffers from problems such as trajectory jumps, strong noise sensitivity, and weak ability to reconstruct long-distance meandering diffusion, which seriously restricts the formulation of regional pollution source tracing and control strategies. Therefore, there is an urgent need for a method that takes into account both physical mechanisms and the advantages of data-driven approaches, and improves the simulation accuracy and reliability of large-scale pollutant transport trajectories through enhanced flow field smoothness and dynamic weight optimization, providing a scientific basis for cross-regional joint prevention and control. Summary of the Invention

[0003] The purpose of this invention is to provide a transmission trajectory method based on flow field smoothness, which solves the problems in the background art.

[0004] This invention is achieved through the following technical solution:

[0005] A transport trajectory method based on flow field smoothness includes the following steps:

[0006] S1. Acquire large-scale wind field data: Acquire large-scale wind field data of the target and establish a coordinate grid. Each grid point is a wind field point, and each wind field point includes the wind speed and wind direction at that point.

[0007] S2. Large-scale wind field data smoothing: Smoothing the wind speed at each wind field point;

[0008] S3. Calculate wind speed weight and wind direction weight: Select a certain wind field point as the initial point, select m wind field points around the initial point as neighboring points, and calculate the wind speed weight and wind direction weight for each neighboring point based on the initial point. The wind speed weight is calculated based on the reciprocal power of the Euclidean distance between the initial point and the neighboring points, and the wind direction weight is calculated based on the cosine similarity of the wind directions between the initial point and the neighboring points.

[0009] S4. Calculate the overall weight: Multiply the wind speed weight and wind direction weight of each neighboring point to obtain the overall weight;

[0010] S5. Trajectory point prediction and update: Calculate the x-axis and y-axis changes of the next nearby point based on the comprehensive weight, wind speed and wind direction of the currently selected nearby point. Obtain the coordinates of the next trajectory point by adding the changes to the current point coordinates. Update the current point as the next trajectory point and repeat the prediction until the required trajectory point is selected.

[0011] S6. Smoothly connect trajectory points: Connect trajectory points sequentially according to the calculation order, and use spline interpolation to ensure the smoothness and continuity of the trajectory.

[0012] This invention acquires large-scale wind field grid data (including wind speed, wind direction, and coordinate information), uses Gaussian smoothing to filter out high-frequency noise, and retains macroscopic flow characteristics. Secondly, it selects neighboring points based on the initial point, and calculates a comprehensive weight by combining the inverse power of spatial distance (wind speed weight) and cosine similarity (wind direction weight), thus doubly constraining the spatial proximity and wind direction consistency of neighboring points. Subsequently, it iteratively predicts the trajectory point position by weighted averaging of the wind speed vectors of neighboring points, dynamically updating the current point until a complete discrete trajectory is generated. Finally, it uses spline interpolation to force the trajectory to be continuously differentiable, eliminating abrupt changes in discrete points and forming a smooth and coherent pollutant transport path.

[0013] Furthermore,

[0014] The wind speed smoothing process includes Gaussian smoothing, which smooths both wind speed and wind direction to reduce high-frequency noise.

[0015] Furthermore,

[0016] The specific steps for calculating the wind speed weight and wind direction weight are as follows:

[0017] S30. Select an initial point and obtain the wind speed and direction at the initial point;

[0018] S31. Select m neighboring points near the initial point and obtain their respective wind speed and wind direction;

[0019] S32. Calculate the wind speed weight and wind direction weight for each neighboring point;

[0020] S33. The comprehensive weight is calculated based on the wind speed weight and wind direction weight.

[0021] Furthermore,

[0022] The wind speed weight is calculated based on spatial distance weighting, and the specific calculation method is as follows: In the formula W Vi d represents the wind speed weight calculated based on spatial distance for the i-th nearest point. iThis represents the Euclidean distance between the initial point and the i-th neighboring point. This represents the decay factor.

[0023] Furthermore,

[0024] The wind direction weight is calculated based on cosine similarity. Cosine similarity can better capture the similarity of wind directions. The specific definition of cosine similarity is: In the formula, θ0 and θ i Let represent the wind direction at the initial point and the wind direction at the i-th neighboring point, respectively.

[0025] Furthermore,

[0026] The specific formula for calculating the comprehensive weight is as follows: In the formula W i W represents the combined weight of the i-th neighboring point. Vi Cosine_similarity(θ0-θ) represents the wind speed weight calculated based on spatial distance to the i-th nearest point. i ) represents the cosine similarity between the wind direction of the i-th neighboring point and the wind direction of the initial point.

[0027] Furthermore,

[0028] Each grid point also includes location coordinate information. The specific steps for predicting and updating the trajectory points are as follows:

[0029] S50. Obtain the position coordinates P of the nearest point currently being processed. K (X k ,Y k );

[0030] S51. Calculate the changes in the x-axis and y-axis of the position of the next nearest point based on the comprehensive weight, wind speed, and wind direction of the currently processed nearest point, and obtain the changes (Δx, Δy);

[0031] S53. Use the coordinates P of the currently processed nearest point. K (X k ,Y k Adding the corresponding change amount yields the coordinates P of the next trajectory point. K+1 (X k+1 ,Y k+1 );

[0032] S54. Update the next nearest point to the current nearest point, go to S50, and continue until the required nearest points are calculated and selected as trajectory points, and record the trajectory point calculation order.

[0033] Furthermore,

[0034] The formulas for calculating the changes (Δx, Δy) are as follows: In the formula W i V represents the combined weight of the i-th neighboring point. i Let θ represent the wind speed at the i-th nearest neighbor point. i Let be the wind direction of the i-th nearest neighbor point.

[0035] Furthermore,

[0036] The attenuation factor The value is greater than or equal to 1 and less than or equal to 2.

[0037] The beneficial effects of this invention are:

[0038] 1. Strong resistance to noise interference: High-frequency noise in wind field data is filtered out by Gaussian smoothing, while large-scale flow characteristics are preserved, which significantly improves the signal-to-noise ratio of the data, avoids trajectory jitter or deviation caused by noise, and enhances the robustness of the method under complex meteorological conditions.

[0039] 2. High physical rationality: The comprehensive weight calculation integrates the inverse power of spatial distance (wind speed weight) and cosine similarity (wind direction weight), which double-constrains the spatial proximity and wind direction consistency of neighboring points, effectively eliminating interference points that are far away or have large differences in wind direction, making the trajectory prediction more in line with the laws of fluid dynamics and reducing path jumps caused by sudden changes in wind direction (such as the passage of a front).

[0040] 3. Excellent accuracy in cross-regional transport: Based on dynamic iterative prediction of weighted average neighboring point wind speed vector, combined with attenuation factor α to flexibly adapt to different grid data, it balances local details and global trends, accurately captures the dominant role of large-scale flow field in the migration of pollutants, and is especially suitable for accurate simulation of long-distance cross-regional transport.

[0041] 4. Excellent trajectory smoothness: The spline interpolation method is used to force the trajectory points to be continuously differentiable, eliminate the jagged abrupt changes of discrete prediction points, generate a smooth and coherent transmission path, restore the true physical characteristics of the roundabout diffusion of pollutants, and provide a highly reliable spatial distribution basis for regional joint prevention and control.

[0042] 5. High flexibility and versatility: The method parameters (attenuation factor) can be dynamically adjusted according to the actual scenario to adapt to uniform wind fields or high-resolution complex wind fields, taking into account both computational efficiency and accuracy requirements, and providing reliable technical support for pollution control strategies in different regions and at different scales. Attached Figure Description

[0043] The accompanying drawings, which are included to provide a further understanding of the embodiments of the present invention and form part of this application, are not intended to limit the embodiments of the present invention.

[0044] Figure 1This is the overall logic flowchart of the present invention;

[0045] Figure 2 A flowchart for calculating wind speed weights and wind direction weights;

[0046] Figure 3 A flowchart for predicting and updating trajectory points. Detailed Implementation

[0047] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0048] See the example. Figures 1 to 3 :

[0049] A transport trajectory method based on flow field smoothness includes the following steps:

[0050] S1. Acquire large-scale wind field data: Acquire large-scale wind field data of the target and establish a coordinate grid. Each grid point is a wind field point, and each wind field point includes the wind speed and wind direction at that point.

[0051] S2. Large-scale wind field data smoothing: Smoothing the wind speed at each wind field point;

[0052] S3. Calculate wind speed weight and wind direction weight: Select a certain wind field point as the initial point, select m wind field points around the initial point as neighboring points, and calculate the wind speed weight and wind direction weight for each neighboring point based on the initial point. The wind speed weight is calculated based on the reciprocal power of the Euclidean distance between the initial point and the neighboring points, and the wind direction weight is calculated based on the cosine similarity of the wind directions between the initial point and the neighboring points.

[0053] S4. Calculate the overall weight: Multiply the wind speed weight and wind direction weight of each neighboring point to obtain the overall weight;

[0054] S5. Trajectory point prediction and update: Calculate the x-axis and y-axis changes of the next nearby point based on the comprehensive weight, wind speed and wind direction of the currently selected nearby point. Obtain the coordinates of the next trajectory point by adding the changes to the current point coordinates. Update the current point as the next trajectory point and repeat the prediction until the required trajectory point is selected.

[0055] S6. Smoothly connect trajectory points: Connect trajectory points sequentially according to the calculation order, and use spline interpolation to ensure the smoothness and continuity of the trajectory.

[0056] Furthermore,

[0057] The wind speed smoothing process includes Gaussian smoothing, which smooths both wind speed and wind direction to reduce high-frequency noise.

[0058] Gaussian smoothing performs low-pass filtering on wind field data through convolution operations, effectively removing high-frequency noise (such as local turbulence or measurement errors) from wind speed and direction data while preserving large-scale flow characteristics. Its core lies in the choice of standard deviation σ: a larger σ results in a wider smoothing range, suitable for uniform wind fields; a smaller σ preserves more details, suitable for complex wind fields. This significantly improves the signal-to-noise ratio of the data, making subsequent weight calculations and trajectory predictions more reliant on realistic macroscopic wind field patterns, avoiding trajectory jitter or deviation caused by noise, thereby enhancing the method's robustness under complex meteorological conditions.

[0059] In one embodiment, the wind speed smoothing process can also employ moving average smoothing, which smooths the wind speed data through window averaging. The specific calculation formula is as follows: In the formula, v represents the smoothed wind speed, n represents the size of the sliding window, i.e. the number of wind field points used to calculate the mean, and v(xi) represents the wind speed of the wind field point in the i-th window.

[0060] Furthermore,

[0061] The specific steps for calculating the wind speed weight and wind direction weight are as follows:

[0062] S30. Select an initial point and obtain the wind speed and direction at the initial point;

[0063] S31. Select m neighboring points near the initial point and obtain their respective wind speed and wind direction;

[0064] S32. Calculate the wind speed weight and wind direction weight for each neighboring point;

[0065] S33. The comprehensive weight is calculated based on the wind speed weight and wind direction weight.

[0066] In one implementation, an initial point P0 is selected, and the wind speed and direction (V0, θ0) and location marking information (X0, Y0) of P0 are obtained. Then, 10 neighboring points are selected around the initial point as the base, and the wind speed and direction (V0, θ0) of each neighboring point are obtained accordingly. i ,θ i Each neighboring point will have its own wind speed weight and wind direction weight calculated separately from the initial point, which will be used to calculate the overall weight.

[0067] Furthermore,

[0068] The wind speed weight is calculated based on spatial distance weighting, and the specific calculation method is as follows: In the formula W Vi d represents the wind speed weight calculated based on spatial distance for the i-th nearest point. i This represents the Euclidean distance between the initial point and the i-th neighboring point. This represents the decay factor.

[0069] Wind speed weighting is based on the inverse power of spatial distance (Euclidean distance), assigning higher weight to neighboring points, which conforms to the physical law of the "nearest neighbor effect." Attenuation factor. Sensitivity to the effects of distance: When =1, the weight decreases linearly with distance, which is suitable for emphasizing the dominant role of close proximity; When the value is 2, the decay exhibits an inverse square ratio, which can suppress interference from distant points. This can be achieved by adjusting... The method can flexibly adapt to grid data with different spatial resolutions, balance local details and global trends, and avoid trajectory prediction deviations caused by over-reliance on neighboring points or ignoring distant information.

[0070] Furthermore,

[0071] The wind direction weight is calculated based on cosine similarity. Cosine similarity can better capture the similarity of wind directions. The specific definition of cosine similarity is: In the formula, θ0 and θ i Let represent the wind direction at the initial point and the wind direction at the i-th neighboring point, respectively.

[0072] Wind direction weights are calculated using cosine similarity, mapping wind direction differences to the [0,1] interval. The weight is maximized (value 1) when the initial point and neighboring points share the same wind direction, and minimized (value 0) when the wind directions are opposite. This method accurately quantifies wind direction similarity, prioritizes neighboring points with the same flow direction as the initial point, ensures the predicted trajectory direction aligns with the prevailing wind trend, avoids path jumps caused by sudden wind changes such as frontal passages, and improves the physical plausibility of cross-regional pollutant transport simulations.

[0073] Furthermore,

[0074] The specific formula for calculating the comprehensive weight is as follows: In the formula W i W represents the combined weight of the i-th neighboring point. Vi Cosine_similarity(θ0-θ) represents the wind speed weight calculated based on spatial distance to the i-th nearest point. i ) represents the cosine similarity between the wind direction of the i-th neighboring point and the wind direction of the initial point.

[0075] The comprehensive weighting achieves dual constraints through the product of wind speed weight and wind direction weight: it considers both the attenuation effect of spatial distance on wind speed and incorporates a screening mechanism for wind direction consistency. This coupled calculation method ensures that the final weight is only effective for grid points that are "nearby and have the same wind direction", eliminating interference points that are far away or have large differences in wind direction. This allows the trajectory prediction to simultaneously satisfy spatial continuity and fluid dynamic consistency, improving the ability to capture pollutant transport paths in complex flow fields.

[0076] Furthermore,

[0077] Each grid point also includes location coordinate information. The specific steps for predicting and updating the trajectory points are as follows:

[0078] S50. Obtain the position coordinates P of the nearest point currently being processed. K (X k ,Y k );

[0079] S51. Calculate the changes in the x-axis and y-axis of the position of the next nearest point based on the comprehensive weight, wind speed, and wind direction of the currently processed nearest point, and obtain the changes (Δx, Δy);

[0080] S53. Use the coordinates P of the currently processed nearest point. K (X k ,Y k Adding the corresponding change amount yields the coordinates P of the next trajectory point. K+1 (X k+1 ,Y k+1 );

[0081] S54. Update the next nearest point to the current nearest point, go to S50, and continue until the required nearest points are calculated and selected as trajectory points, and record the trajectory point calculation order.

[0082] Furthermore,

[0083] The formulas for calculating the changes (Δx, Δy) are as follows: In the formula W i V represents the combined weight of the i-th neighboring point. i Let θ represent the wind speed at the i-th nearest neighbor point. i Let be the wind direction of the i-th nearest neighbor point.

[0084] The changes Δx and Δy are calculated by projecting the wind speed vectors of each neighboring point onto the x and y axes with comprehensive weights. Essentially, this is a weighted average of the wind field vectors to accurately predict the changes of the next trajectory point based on the current point's x and y axes. The position coordinates of the next trajectory point are calculated based on the current point's position coordinates. Each iteration is based on the current point's position and the weighted average wind field vector, ensuring that the trajectory is continuous and conforms to the actual flow trend. This effectively simulates the dynamic migration process of pollutants in complex wind fields.

[0085] Furthermore,

[0086] The attenuation factor The value is greater than or equal to 1 and less than or equal to 2.

[0087] Furthermore,

[0088] The smooth connection trajectory points are connected sequentially according to the calculation order, and spline interpolation is used to ensure the smoothness and continuity of the trajectory.

[0089] Spline interpolation fits discrete trajectory points using piecewise polynomial functions, forcing the curve to have continuous first and second derivatives at the connection points, thereby eliminating abrupt, polygonal changes in the trajectory and generating a smooth, continuous transmission path. This step compensates for the sawtooth effect caused by the discretization of prediction points, ensuring that the trajectory visually and physically conforms to the smoothness characteristics of fluids. Especially in simulations of long-distance, cross-regional transmission, spline interpolation can effectively reconstruct the circuitous diffusion paths of pollutants, providing highly reliable spatial distribution data for joint prevention and control.

[0090] In another embodiment, Bézier curves are used to smoothly connect trajectory points, which can effectively connect irregular trajectory points to obtain a smooth pollutant transport trajectory.

[0091] It is understood that the above embodiments are merely exemplary implementations used to illustrate the principles of the present invention, and the present invention is not limited thereto. For those skilled in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also considered to be within the scope of protection of the present invention.

Claims

1. A transport trajectory method based on flow field smoothness, characterized in that, Includes the following steps: S1. Acquire large-scale wind field data: Acquire large-scale wind field data of the target and establish a coordinate grid. Each grid point is a wind field point, and each wind field point includes the wind speed and wind direction at that point. S2. Large-scale wind field data smoothing: Smoothing the wind speed at each wind field point; S3. Calculate wind speed weight and wind direction weight: Select a certain wind field point as the initial point, select m wind field points around the initial point as neighboring points, and calculate the wind speed weight and wind direction weight for each neighboring point based on the initial point. The wind speed weight is calculated based on the reciprocal power of the Euclidean distance between the initial point and the neighboring points, and the wind direction weight is calculated based on the cosine similarity of the wind directions between the initial point and the neighboring points. S4. Calculate the overall weight: Multiply the wind speed weight and wind direction weight of each neighboring point to obtain the overall weight; S5. Trajectory point prediction and update: Calculate the x-axis and y-axis changes of the next nearby point based on the comprehensive weight, wind speed and wind direction of the currently selected nearby point. Obtain the coordinates of the next trajectory point by adding the changes to the current point coordinates. Update the current point as the next trajectory point and repeat the prediction until the required trajectory point is selected. S6. Smoothly connect trajectory points: Connect trajectory points sequentially according to the calculation order, and use spline interpolation to ensure the smoothness and continuity of the trajectory.

2. The transport trajectory method based on flow field smoothness according to claim 1, characterized in that, The wind speed smoothing process includes Gaussian smoothing, which smooths both wind speed and wind direction to reduce high-frequency noise.

3. The transport trajectory method based on flow field smoothness according to claim 1, characterized in that, The specific steps for calculating the wind speed weight and wind direction weight are as follows: S30. Select an initial point and obtain the wind speed and direction at the initial point; S31. Select m neighboring points near the initial point and obtain their respective wind speed and wind direction; S32. Calculate the wind speed weight and wind direction weight for each neighboring point; S33. The comprehensive weight is calculated based on the wind speed weight and wind direction weight.

4. The transport trajectory method based on flow field smoothness according to claim 3, characterized in that, The wind speed weight is calculated based on spatial distance weighting, and the specific calculation method is as follows: In the formula W Vi represents the wind speed weight of the i-th neighboring point calculated based on spatial distance, and di represents the Euclidean distance between the initial point and the i-th neighboring point. This represents the decay factor.

5. The transport trajectory method based on flow field smoothness according to claim 4, characterized in that, The wind direction weight is calculated based on cosine similarity. Cosine similarity can better capture the similarity of wind directions. The specific definition of cosine similarity is: In the formula, θ0 and θ i Let represent the wind direction at the initial point and the wind direction at the i-th neighboring point, respectively.

6. The transport trajectory method based on flow field smoothness according to claim 5, characterized in that, The specific formula for calculating the comprehensive weight is as follows: In the formula W i W represents the combined weight of the i-th neighboring point. Vi Cosine_similarity(θ0-θ) represents the wind speed weight calculated based on spatial distance to the i-th nearest point. i ) represents the cosine similarity between the wind direction of the i-th neighboring point and the wind direction of the initial point.

7. The transport trajectory method based on flow field smoothness according to claim 1, wherein each grid point further includes position coordinate information, characterized in that, The specific steps for predicting and updating trajectory points are as follows: S50. Obtain the position coordinates P of the nearest point currently being processed. K (X k ,Y k ); S51. Calculate the changes in the x-axis and y-axis of the position of the next nearest point based on the comprehensive weight, wind speed, and wind direction of the currently processed nearest point, and obtain the changes (Δx, Δy); S53. Use the coordinates P of the currently processed nearest point. K (X k ,Y k Adding the corresponding change amount yields the coordinates P of the next trajectory point. K+1 (X k+1 ,Y k+1 ); S54. Update the next nearest point to the current nearest point, go to S50, and continue until the required nearest points are calculated and selected as trajectory points, and record the trajectory point calculation order.

8. The transport trajectory method based on flow field smoothness according to claim 7, characterized in that, The formulas for calculating the changes (Δx, Δy) are as follows: In the formula, Wi represents the combined weight of the i-th neighboring point, and V i Let θ represent the wind speed at the i-th nearest neighbor point. i Let be the wind direction of the i-th nearest neighbor point.

9. The transport trajectory method based on flow field smoothness according to claim 4, characterized in that, The attenuation factor The value is greater than or equal to 1 and less than or equal to 2.

Images