Prediction method of three-dimensional complex terrain wind field
By constructing terrain feature vectors and similar wind field data, and combining environmental factors and physically constrained neural networks (PINN), the problem of high accuracy and speed in wind field prediction under complex three-dimensional terrain was solved, achieving high accuracy, physical consistency and fast computation capability in wind field prediction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- THREE GORGES JINSHAJIANG CHUANYUN HYDROPOWER DEV CO LTD
- Filing Date
- 2026-02-11
- Publication Date
- 2026-05-19
AI Technical Summary
Existing technologies struggle to achieve high-precision, physically consistent, and rapid wind field prediction in complex 3D terrains. They lack the ability to utilize wind fields in similar terrains and adapt to environment-driven models. Furthermore, deep models do not incorporate fluid dynamics constraints, resulting in predictions that do not conform to fundamental physical laws.
By constructing a terrain feature vector, combining similar wind field data and environmental factors, and training it using a Physically Constrained Neural Network (PINN), wind field prediction is achieved by introducing continuity and momentum equation constraints.
It improves the accuracy and physical rationality of wind field prediction, enhances the model's generalization ability and computational efficiency, adapts to the rapid assessment needs of various terrains and environments, and is applicable to engineering scenarios such as wind energy resource assessment and urban ventilation design.
Smart Images
Figure CN122064993A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the fields of terrain analysis and machine learning technology, and in particular to a method for predicting wind fields in three-dimensional complex terrain. Background Technology
[0002] The spatial distribution of wind speed and direction in complex 3D terrain is influenced by topographic relief, roughness variations, building clusters, and surface thermal conditions. Existing wind field prediction techniques mainly include numerical simulation (RANS, LES), empirical models, and purely data-driven models. While CFD methods based on the Navier-Stokes equations offer high accuracy, they are computationally intensive and cannot meet the demands for rapid multi-scheme prediction in complex terrain and large spatial scales. Empirical methods rely on simplified wind speed profiles and statistical regularities, making it difficult to reflect local effects such as ridge bypass, canyon acceleration, and building interference. Data-driven methods, while fast, lack physical constraints, easily generating physically inconsistent wind speed fields in extrapolated scenarios, and exhibit weak generalization ability when samples are insufficient. Furthermore, existing technologies still have shortcomings in the following aspects: They lack full utilization of prior wind fields from similar terrains; while there is transferability between wind fields from different terrains, traditional methods do not construct standardized terrain feature vectors for retrieving similar scenarios; they lack "environment-driven (wind speed, wind direction, atmospheric stability) model adaptation capabilities," making it difficult for models to make unified predictions of wind fields under different weather conditions; and deep models do not incorporate fluid dynamics physical constraints, leading to prediction results that may violate basic physical laws. In summary, existing technologies struggle to simultaneously achieve high accuracy, physical consistency, and rapid prediction in complex 3D terrains, failing to meet the dual requirements of computational efficiency and accuracy in engineering projects. Summary of the Invention
[0003] In view of this, this application provides a method for predicting wind fields in three-dimensional complex terrain by integrating terrain coding, environment-driven, similar scene transfer and physical constraint neural networks. By combining prior knowledge of wind fields in similar historical terrains with environmental condition correction, and by adding continuity equations and momentum equation constraints during model training, the predicted wind field has both high accuracy and conforms to the basic laws of fluid mechanics, thereby meeting the comprehensive requirements of wind field prediction in engineering practice for speed, high accuracy and high physical consistency.
[0004] This application discloses a method for predicting wind fields in three-dimensional complex terrain, which includes: Step 1: Obtain the elevation matrix by processing the Digital Elevation Model (DEM) corresponding to the complex terrain of the target. Based on the elevation matrix... ， The gradient and slope of the terrain are obtained, and the terrain feature vector corresponding to the complex terrain of the target is obtained based on the gradient and slope of the terrain. Step 2: Obtain a set of similar wind field data based on the terrain feature vectors corresponding to the complex terrain of the target; Step 3: Obtain the prior wind field based on the similar wind field data set; Step 4: Input the terrain feature vector and prior wind field into the Physically Constrained Neural Network (PINN) to obtain the three-dimensional wind speed. Based on the three-dimensional wind speed, obtain the total loss of the Physically Constrained Neural Network (PINN). By minimizing the total loss, obtain the trained PINN model. Step 5: Construct a three-dimensional computational domain within the new target complex terrain area, and divide the three-dimensional computational domain into several sets of spatial grid points to be predicted. Input each spatial grid point in the set of spatial grid points, its corresponding terrain feature vector, and the prior wind field into the trained PINN model to obtain the three-dimensional wind speed corresponding to each spatial grid point, and finally obtain the wind field of the new target complex terrain area.
[0005] Further, step 1 includes: Step 11: Calculate the gradient of the elevation matrix H in the x and y directions: ,
[0006] in, S x and S y The x and y axes represent the east-west and north-south gradients, respectively. The origin of the global unified spatial coordinate system is the reference starting point of the terrain data in the horizontal projection plane, that is, a boundary corner point within the horizontal projection range of the terrain. The x-axis represents the east-west direction of the terrain, the y-axis represents the north-south direction of the terrain, and the z-axis represents the height of the terrain. The slope is obtained from the gradient using the following formula:
[0007] Here, slope indicates the degree of local terrain slope; Step 12: Obtain the surface roughness intensity based on the elevation matrix H; Step 13: Obtain the TRI index based on the elevation value of the grid point to be evaluated and the elevation values of its neighboring grid points; Step 14: Based on the surface roughness intensity, slope, surface roughness intensity, and TRI index, obtain the terrain feature vector corresponding to the target complex terrain.
[0008] Further, step 12 includes: The surface roughness intensity is obtained using an empirical formula based on the standard deviation of elevation. :
[0009] Among them, std(H ) represents the standard deviation of the elevation matrix; Step 13 includes: Surface classification data is converted into one-hot encoding to distinguish surface types; surface types include water bodies, vegetation, bare land, and built-up areas; surface classification data includes surface type information obtained through remote sensing imagery, topographic surveys, or other geographic information systems (GIS); The TRI index, used to describe the intensity of terrain undulation, is obtained through the following formula:
[0010] in, () represents the elevation value of the grid point to be evaluated. express Within the neighborhood The elevation values of each grid point are given, where M is the total number of grid points in the neighborhood participating in the calculation. Step 14 includes: The terrain feature vector is obtained using the following formula:
[0011] Where T is the terrain feature vector corresponding to the target complex terrain, and one-hot is the one-hot encoding of the land surface type.
[0012] Further, step 2 includes: Step 21: Combine the feature vectors of multiple terrain regions The corresponding wind field data Paired storage is performed to form a terrain-wind field sample library; Step 22: Based on the Euclidean distance between the terrain feature vector corresponding to the target complex terrain and the feature vector in the terrain-wind field sample library, select a preset number of terrain regions from the terrain-wind field sample library, and construct a similar wind field data set by combining the wind field data corresponding to the preset number of terrain regions.
[0013] Further, step 3 includes: Step 31: In wind field prediction, an environmental feature vector is constructed based on environmental factors, including incoming wind speed, incoming wind direction, atmospheric stability, and surface temperature. Step 32: Convert the environmental feature vector into response values for similar wind fields using the weighted generation network (WGN); Step 33: Obtain the corresponding weights based on the response values of similar wind fields; Step 34: Based on the weights and the corresponding wind field data in the similar wind field dataset, obtain the prior wind field obtained under the combined effect of the terrain feature vector and the environmental feature vector corresponding to the target complex terrain.
[0014] Further, step 32 includes: The response values for similar wind fields can be obtained using the following formula:
[0015] in, Represents the first element in a set of similar wind field data under environmental conditions. The response level of a wind field, where k represents the total number of similar wind field data in the similar wind field dataset; Step 33 includes: Use Softmax to generate normalized weights:
[0016] in, This represents the normalized weight of the i-th wind field in the similar wind field dataset under the current environmental conditions. Represents the first element in a set of similar wind field data under environmental conditions. The degree of response to similar wind fields; Step 34 includes: The prior wind field is obtained using the following formula:
[0017] in, The weights represent the prior wind field obtained under the combined influence of terrain feature vector T and environmental feature vector E. Indicates the effect of environmental conditions on the first The adjustment coefficient of each wind field.
[0018] Further, step 4 includes: Step 41: Input the terrain feature vector and prior wind field into the Physically Constrained Neural Network (PINN) to obtain the three-dimensional wind speed; Step 42: Based on the prior wind field and the actual wind field, obtain the data error term; Step 43: Based on the three-dimensional wind speed, obtain the continuity loss and momentum residual; Step 44: Obtain the momentum loss based on the momentum residual; Step 45: Obtain the total loss based on the data error term, continuity loss, and momentum loss; Step 46: By minimizing the total loss, the trained PINN model is obtained.
[0019] Further, step 42 includes: The data error term is obtained using the following formula:
[0020] in, This represents the data error term, used to measure the model's prediction of the prior wind field. With real wind field The differences between them; Step 43 includes: The continuity loss is obtained using the following formula. :
[0021] in, Indicates the divergence of the wind field. Approaching zero to ensure that the predicted wind field satisfies the continuity condition of incompressible flow; This represents the wind speed component in one dimension of a three-dimensional wind speed. The gradient operator with respect to spatial coordinates is used to describe the rate of change of a physical quantity in space; The momentum residual is obtained using the following formula. for:
[0022] in, The pressure scalar field representing the pressure field in the wind field is the pressure term in the momentum equation of an incompressible fluid; air density, For dynamic viscosity, For volume forces, This indicates the degree of deviation of the momentum equation from the current predicted wind field, and is used to measure whether the output of the PINN model satisfies the momentum conservation equation for incompressible fluids. This represents the convection term, describing the spatial variation of fluid velocity as it moves. The Laplace operator is used to describe momentum diffusion; Step 44 includes: The momentum loss is obtained using the following formula:
[0023] in, Indicates momentum loss; Step 45 includes: The total loss is obtained using the following formula:
[0024] in, For the total loss, These are the weighting coefficients.
[0025] Further, step 5 includes: Step 51: Construct a 3D computational domain within the new target complex terrain region. and in the three-dimensional computational domain The space is divided into several sets G of spatial grid points to be predicted according to the given horizontal and vertical resolution:
[0026] in, Indicates the first There are N spatial grid points, where N is the total number of grid points in each set G. The three-dimensional spatial extent of the new target complex terrain region; For a globally unified spatial coordinate system The three coordinate components; Step 52: Combine each spatial grid point in the spatial grid point set G with the corresponding terrain feature vector and prior wind field information to form the input vector of the Physically Constrained Neural Network (PINN); Let the first... The input of the grid points is :
[0027] in, For the first The input vector of spatial grid points Indicates at spatial grid points The surrounding local terrain feature vector is obtained by encoding the terrain feature vector. This indicates the prior wind field obtained by weighting environmental feature vectors at spatial grid points. Interpolated value or nearest neighbor value at the location; Physically constrained neural networks (PINN) are considered as having parameters. The nonlinear mapping function will... Input of spatial grid points The mapping is to a three-dimensional wind speed output, which takes the following form:
[0028] in, For a well-trained PINN model, For the PINN model at spatial grid points The predicted three-dimensional wind speed vector is obtained at that location. These are the wind speed components of the three-dimensional wind speed vector in three directions; By all By performing forward reasoning, the predicted wind field for the entire new target complex terrain area can be obtained in one go.
[0029] Furthermore, after step 5, the method further includes: vector set All or part of Composition matrix And calculate the set of wind speed vectors obtained by performing one or more forward inference operations. :
[0030] in, In the three-dimensional computational domain The set of predicted wind speed vectors at all spatial grid points is considered to be of size . The matrix, Each row of the matrix corresponds to the three-dimensional wind speed of a spatial grid point; Will Remapping back to the spatial coordinate system, construct a discrete wind field function defined on Ω. If you need to adjust any position in the spatial coordinate system Interpolation will then determine the discrete wind speed. Convert to continuous field function This makes the wind field more smooth and continuous in visualization and post-processing analysis; Obtaining the three-dimensional wind speed vector Then, calculate the wind speed amplitude:
[0031] in, For the first The wind speed at each spatial grid point is used for wind energy density and wind environment assessment. , , Representing discrete wind speeds The three components; For wind energy applications, calculate the wind power density per unit volume:
[0032] in, For the first Wind power density at each spatial grid point For the first Unit volume at each spatial grid point Air density is used to characterize the abundance of wind resources. If it is necessary to analyze relevant indicators, the ratio of wind speed variance to mean is calculated in a local neighborhood or time dimension to obtain an approximate estimate of turbulence intensity, which is used for wind turbine fatigue load and comfort assessment. Relevant indicators include turbulence intensity. Step 5.5: For arbitrary spatial grid points in the prediction phase Calculate the numerical divergence:
[0033] in, To predict wind field at spatial grid points The divergence value is used to evaluate whether the prediction results satisfy the incompressibility condition; Spatial grid points One of the coordinate components; By statistically analyzing the divergence distribution across the entire grid corresponding to the new target complex terrain area, it is determined whether there are physically inconsistent regions in the prediction of the PINN model. If there are no physically inconsistent regions, the physical test is passed, and the predicted wind field and its derived indices can be used in relevant engineering scenarios. Relevant engineering scenarios include wind energy site selection, urban ventilation corridor planning, or building wind load analysis.
[0034] Due to the adoption of the above technical solution, this application has the following advantages: 1. Improve the reliability of wind field prediction in complex terrain: This application constructs a unified terrain feature coding system, enabling key information such as slope, roughness, surface type, and local undulations of complex terrain to be input into the model in a structured manner, thereby overcoming the limitation of traditional empirical models that cannot accurately represent terrain differences. At the same time, combined with a similar terrain retrieval mechanism, the model can still maintain a stable expression of wind speed distribution structure by utilizing historical terrain and prior wind field information even when data is insufficient, complex terrain differences are significant, or measured data are lacking. This makes the overall prediction theoretically more robust and adaptable to different scenarios, which is conducive to improving the model's ability to identify and maintain consistency of wind fields in different types of terrain.
[0035] 2. Improving the accuracy and physical plausibility of wind field prediction: This application combines an environment-driven dynamic weight generation method to enable the prior wind field to adaptively adjust to changes in incoming wind speed, wind direction, and atmospheric stability, allowing the prediction model to adjust the wind field structure according to meteorological conditions. At the same time, a Physically Constrained Neural Network (PINN) is introduced. During the training process, the residual constraints of the continuity equation and momentum equation ensure that the wind speed field output by the model maintains consistency with fluid dynamics in terms of velocity gradient, divergence distribution, and local vortex structure. This reduces common problems in pure data-driven models, such as velocity abrupt changes, divergence imbalance, and local anomalous vortices, thereby improving the overall accuracy and theoretical physical reliability of wind field prediction.
[0036] 3. Improve computational efficiency and meet the needs of rapid large-scale wind field prediction: This application combines similar terrain priors with physical constraint deep learning methods, so that the three-dimensional wind field prediction does not require the traditional CFD grid solution process. Instead, it directly obtains the three-dimensional wind speed field of the entire area through the forward computation of neural networks, which significantly improves the prediction speed. Theoretically, this method can complete large-scale wind field simulation under multiple wind directions and multiple wind speeds in a short time. It is suitable for rapidly assessing wind energy resources, urban ventilation conditions and wind environment response of building clusters, and provides efficient support for engineering scenarios that require a large number of scheme comparisons or real-time analysis.
[0037] 4. Improve the generalization ability of the model and enhance its engineering applicability: This application combines terrain coding with similar terrain priors to enable the wind field prediction model to have higher generalization potential in various scenarios such as complex mountains, canyons, and building cluster disturbances; combined with environmental driving mechanisms and physical constraint structures, the model can adapt to the wind field prediction needs under multiple terrains and environmental parameters, and theoretically can provide a highly operable and stable wind field prediction method for multiple engineering fields such as wind energy resource assessment, urban wind environment design, and aerodynamic analysis. Attached Figure Description
[0038] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings.
[0039] Figure 1 This is a flowchart illustrating a method for predicting wind fields in three-dimensional complex terrain, as described in an embodiment of this application. Detailed Implementation
[0040] The present application will be further described in conjunction with the accompanying drawings and embodiments. The described embodiments are only some, not all, of the embodiments of the present application. All other embodiments obtained by those skilled in the art should fall within the protection scope of the embodiments of the present application.
[0041] See Figure 1 This application provides an embodiment of a method for predicting wind fields in three-dimensional complex terrain, which includes: Step 1: Obtain the elevation matrix by processing the Digital Elevation Model (DEM) corresponding to the complex terrain of the target. Based on the elevation matrix... ， The gradient and slope of the terrain are obtained, and the terrain feature vector corresponding to the complex terrain of the target is obtained based on the gradient and slope of the terrain. Step 2: Obtain a set of similar wind field data based on the terrain feature vectors corresponding to the complex terrain of the target; Step 3: Obtain the prior wind field based on the similar wind field data set; Step 4: Input the terrain feature vector and prior wind field into the Physically Constrained Neural Network (PINN) to obtain the three-dimensional wind speed. Based on the three-dimensional wind speed, obtain the total loss of the Physically Constrained Neural Network (PINN). By minimizing the total loss, obtain the trained PINN model. Step 5: Construct a three-dimensional computational domain within the new target complex terrain area, and divide the three-dimensional computational domain into several sets of spatial grid points to be predicted. Input each spatial grid point in the set of spatial grid points, its corresponding terrain feature vector, and the prior wind field into the trained PINN model to obtain the three-dimensional wind speed corresponding to each spatial grid point, and finally obtain the wind field of the new target complex terrain area.
[0042] Optionally, step 1 includes: Step 11: Calculate the gradient of the elevation matrix H in the x and y directions to obtain the trend of terrain change in both directions: ,
[0043] in, S x and S y The x and y axes represent the east-west and north-south gradients, respectively (reflecting the terrain slope, gradient, and degree of surface undulation, which are important indicators affecting wind acceleration, flow around, and separation phenomena). The x and y axes represent the x-axis and y-axis in the global unified spatial coordinate system, respectively. The origin of the global unified spatial coordinate system (a reference point in the global unified spatial coordinate system) is the reference starting point of the terrain data in the horizontal projection plane, that is, a boundary corner point within the horizontal projection range of the terrain. The x-axis represents the east-west direction (longitude) of the terrain, the y-axis represents the north-south direction (latitude) of the terrain, and the z-axis represents the height (vertical direction) of the terrain. Based on the gradient, the slope is obtained using the following formula, which comprehensively reflects the terrain slope and its impact on wind flow distribution:
[0044] Among them, slope represents the degree of local terrain inclination. In steep slope areas, wind speed often increases or leeward side vortex structures appear. Therefore, slope is an indispensable basic feature for wind field prediction. Step 12: Obtain the surface roughness intensity based on the elevation matrix H; Step 13: Obtain the TRI index based on the elevation value of the grid point to be evaluated and the elevation values of its neighboring grid points; Step 14: Based on the surface roughness intensity, slope, surface roughness intensity, and TRI index, obtain the terrain feature vector corresponding to the target complex terrain.
[0045] Optionally, step 12 includes: The roughness of the terrain surface directly affects the attenuation characteristics of near-surface wind speed. The surface roughness intensity is obtained using an empirical formula based on the standard deviation of elevation. :
[0046] Among them, std( H The standard deviation of the elevation matrix reflects the degree of surface undulation; surface roughness intensity. Used to characterize the wind speed attenuation characteristics of the friction layer, enabling the model to learn the specific impact of different terrains on wind speed based on roughness differences; Step 13 includes: To differentiate regional surface material variations, surface classification data is converted into one-hot encoding to distinguish surface types. Surface types include water bodies, vegetation, bare land, and built-up areas. Surface classification data includes surface type information obtained through remote sensing imagery, topographic surveys, or other geographic information systems (GIS). Surface classification data is typically based on surface cover characteristics such as soil type, topography, and land use. Specific classifications may include the following categories: water bodies, vegetation, bare land, built-up areas, agricultural land, roads, and rocks. The TRI index, used to describe the intensity of terrain undulation, is obtained through the following formula:
[0047] in, () represents the elevation value of the grid point to be evaluated. express Within the neighborhood The elevation values of each grid point are M, which is the total number of grid points in the neighborhood participating in the calculation. The TRI index measures the degree of deviation of the elevation of each grid point in the local area from the central elevation, thereby characterizing the intensity of topographic relief and reflecting the potential impact of rugged terrain on wind speed changes and turbulence structure. Step 14 includes: The terrain feature vector is obtained using the following formula:
[0048] Where T is the terrain feature vector corresponding to the target complex terrain, and one-hot is the one-hot encoding of the land surface type.
[0049] By unifying the aforementioned multi-source terrain attributes into a terrain feature vector T, the terrain of different regions can be standardized and represented in a unified space, providing a consistent input description for similar terrain retrieval and subsequent wind field prediction models.
[0050] Optionally, by extracting terrain gradients and slopes, the geometry of complex regional terrain can be obtained in a quantifiable manner.
[0051] Optionally, step 2 includes: Step 21: In order to effectively utilize the wind field information of historical regions, the feature vectors of multiple terrain regions are... The corresponding wind field data Paired storage is performed to construct a terrain-wind field sample library. The construction method of the terrain-wind field sample library supports both wind fields based on CFD simulations and measured data based on anemometer towers or lidar. The data structure constructed in this step will serve as the foundation of the entire retrieval system, enabling new terrain features to extract reference wind fields with similar flow field structures from historical data. Step 22: Based on the Euclidean distance between the terrain feature vector corresponding to the target complex terrain and the feature vector in the terrain-wind field sample library, select a preset number of terrain regions from the terrain-wind field sample library, and construct a similar wind field data set by combining the wind field data corresponding to the preset number of terrain regions.
[0052] Specifically, step 22 includes: Using Euclidean distance as the metric, its calculation method is as follows:
[0053] in, This indicates the degree of geometric difference between the target terrain and the sample terrain. The smaller the value, the more similar the terrain features of the two terrains. This step achieves fast similar terrain retrieval through numerical methods; Sort by Euclidean distance, select the k (up to 5) sample regions with the smallest distance to form a set of similar wind fields:
[0054] in, The wind field corresponding to similar terrain can serve as a structural feature reference, improving the stability and accuracy of wind field prediction. This step ensures that the target wind field prediction has a priori basis in terrain structure.
[0055] Optionally, step 3 includes: Step 31: In wind field prediction, an environmental feature vector is constructed based on environmental factors, including incoming wind speed, incoming wind direction, atmospheric stability, and surface temperature. Step 32: Convert the environmental feature vector into response values for similar wind fields using the weighted generation network (WGN); Step 33: Obtain the corresponding weights based on the response values of similar wind fields; Step 34: Based on the weights and the corresponding wind field data in the similar wind field dataset, obtain the prior wind field obtained under the combined effect of the terrain feature vector and the environmental feature vector corresponding to the target complex terrain.
[0056] Optionally, step 31 includes: In wind field prediction, environmental factors such as incoming wind speed, incoming wind direction, atmospheric stability, and surface temperature have a significant impact on wind field structure. Therefore, these parameters are used to construct an environmental feature vector:
[0057] Where U represents the incoming air velocity. Indicates the direction of the incoming wind, and L represents atmospheric stability. For surface temperature. This step provides the necessary input for subsequent weight generation, enabling wind field predictions to adapt to environmental changes; Optionally, step 32 includes: The response values for similar wind fields can be obtained using the following formula:
[0058] in, Represents the first element in a set of similar wind field data under environmental conditions. The response level of each wind field forms the basis for the subsequent weighting mechanism; k represents the total number of similar wind field data in the similar wind field dataset; Step 33 includes: Use Softmax to generate normalized weights:
[0059] in, This represents the normalized weight of the i-th wind field in the similar wind field dataset under the current environmental conditions, determined by the response degree. The Softmax transformation is used to proportionally allocate the importance of different similar wind fields according to environmental factors, so that the weights remain non-negative and reflect the relative contribution of each wind field to the overall prior structure. Represents the first element in a set of similar wind field data under environmental conditions. The degree of response to similar wind fields; Step 34 includes: The prior wind field is obtained using the following formula:
[0060] in, The weights represent the prior wind field obtained under the combined influence of terrain feature vector T and environmental feature vector E. Indicates the effect of environmental conditions on the first The adjustment coefficients of each wind field are calculated; by weighted summation of each similar wind field, a reference wind field (prior wind field) with both structural prior and environmental adaptability is generated, providing a data foundation with stronger physical consistency for the subsequent PINN model.
[0061] Optionally, step 4 includes: Step 41: Input the terrain feature vector and prior wind field into the Physically Constrained Neural Network (PINN) to obtain the three-dimensional wind speed; Step 42: Based on the prior wind field and the actual wind field, obtain the data error term; Step 43: Based on the three-dimensional wind speed, obtain the continuity loss and momentum residual; Step 44: Obtain the momentum loss based on the momentum residual; Step 45: Obtain the total loss based on the data error term, continuity loss, and momentum loss; Step 46: By minimizing the total loss, the trained PINN model is obtained.
[0062] Optionally, step 41 includes: The PINN model combines the terrain feature vector T with the prior wind field. As input:
[0063] The input consists of the terrain feature vector T and the prior wind field F obtained by weighting based on similar wind fields. prior Together, they form a composite input that provides the neural network with information on the regional topographic structure and wind field background, enabling the model to learn the nonlinear mapping relationship between topographic changes and wind speed distribution within a unified input space. By introducing a composite input form that simultaneously includes topographic structure features and wind field structure priors, the model's ability to express the wind flow organization patterns in complex terrain can be enhanced, and a more physically consistent feature basis can be provided for subsequent prediction of three-dimensional wind speed components. The output wind speed is:
[0064] Where u, v, and w represent the three-dimensional wind speed components, respectively.
[0065] Optionally, step 42 includes: The data error term is obtained using the following formula:
[0066] in, This represents the data error term, used to measure the model's prediction of the prior wind field. With real wind field The difference between them is expressed as the squared error of both over the entire domain. By minimizing this loss, the model output wind speed field can be made to approximate the reference wind field in terms of both overall distribution and local features, thereby ensuring that the prediction results have sufficient accuracy at the data level. Step 43 includes: The continuity loss is obtained using the following formula. :
[0067] in, Indicates the divergence of the wind field. Approaching zero to ensure that the predicted wind field satisfies the continuity condition of incompressible flow; This represents the wind speed component in one dimension of a three-dimensional wind speed. The gradient operator with respect to spatial coordinates is used to describe the rate of change of physical quantities in space. By adding a continuous loss during training, the non-physical velocity source and sink structure generated by the model can be effectively suppressed, so that the prediction results maintain the mass conservation characteristics as a whole, and provide a physically consistent basis for subsequent momentum equation constraints. The momentum residual is obtained using the following formula. for:
[0068] in, It represents the pressure (static pressure) scalar field in the wind field and is the pressure term in the momentum equation of incompressible fluids; air density, For dynamic viscosity, For volume forces, This indicates the degree of deviation of the momentum equation from the current predicted wind field, and is used to measure whether the output of the PINN model satisfies the momentum conservation equation for incompressible fluids. Represents the convection (inertia) term, describing the spatial variation of fluid velocity as it moves. The Laplace operator is used to describe momentum diffusion (viscous effect). Step 44 includes: The momentum loss is obtained using the following formula:
[0069] in, This represents momentum loss; the momentum loss is used to constrain the wind speed and pressure fields generated by the model to conform to the fluid dynamics equations, so that the prediction results have higher physical consistency in terms of velocity gradient, pressure distribution and flow field structure. Step 45 includes: The total loss is obtained using the following formula:
[0070] in, For the total loss, The weighting coefficients are used to balance the relative contributions of physical constraint terms and data error terms, enabling the model to fit real wind field data while maintaining continuity and momentum conservation. By comprehensively optimizing the total loss, a reasonable trade-off between data accuracy and physical consistency can be achieved, thereby improving the reliability and stability of the final 3D wind field prediction.
[0071] Optionally, step 5 includes: Step 51: Construct a 3D computational domain within the new target complex terrain region. and in the three-dimensional computational domain The space is divided into several sets G of spatial grid points to be predicted according to the given horizontal and vertical resolution:
[0072] in, Indicates the first There are N spatial grid points, where N is the total number of grid points in each set G. The three-dimensional spatial extent of the new target complex terrain region; For a globally unified spatial coordinate system The three coordinate components; by dividing such a set of grid points, the wind field of the entire region can be predicted based solely on the set of points without explicitly constructing a finite volume or finite element control volume. At the same time, by controlling the density and distribution of G, the model can have higher spatial resolution in key areas such as steep slope changes, canyon shrinkage, and dense buildings, while the grid density can be appropriately relaxed in areas with relatively flat terrain or gentle flow field changes, thereby achieving a balance between prediction accuracy and computational cost. Step 52: Combine each spatial grid point in the spatial grid point set G with the corresponding terrain feature vector and prior wind field information to form the input vector of the Physically Constrained Neural Network (PINN); Let the first... The input of the grid points is :
[0073] in, For the first The input vector of spatial grid points Indicates at spatial grid points The surrounding local terrain feature vector is obtained by encoding the terrain feature vector. This indicates the prior wind field obtained by weighting environmental feature vectors at spatial grid points. Interpolated value or nearest neighbor value at the location; Physically constrained neural networks (PINN) are considered as having parameters. The nonlinear mapping function will... Input of spatial grid points The mapping is to a three-dimensional wind speed output, which takes the following form:
[0074] in, For a well-trained PINN model, For the PINN model at spatial grid points The predicted three-dimensional wind speed vector is obtained at that location. These are the wind speed components of the three-dimensional wind speed vector in three directions; By all By performing forward reasoning, the predicted wind field for the entire new target complex terrain area can be obtained in one go.
[0075] Optionally, after step 5, the method further includes: In engineering applications, to improve prediction efficiency, the model is not called point by point individually; instead, a set of vectors is used. All or part of Composition matrix The wind speed vector set is obtained by performing one or more forward inference operations on a GPU or other accelerated hardware through vectorized computation. :
[0076] in, In the three-dimensional computational domain The set of predicted wind speed vectors at all spatial grid points can be considered as having a size of The matrix, Each row of the matrix corresponds to the three-dimensional wind speed of a spatial grid point; After the prediction is completed, it can be Remapping back to the spatial coordinate system, construct a discrete wind field function defined on Ω. If you need to adjust any position in the spatial coordinate system For interpolation, methods such as nearest neighbor-based, inverse distance weighted, or spline interpolation can be used to interpolate discrete wind speeds. Convert to continuous field function This makes the wind field more smooth and continuous in visualization and post-processing analysis; Obtaining the three-dimensional wind speed vector Next, calculate the wind field derivatives commonly used in engineering. First, calculate the wind speed amplitude:
[0077] in, For the first The wind speed at each spatial grid point is used for wind energy density and wind environment assessment. , , Representing discrete wind speeds The three components; For wind energy applications, calculate the wind power density per unit volume:
[0078] in, For the first Wind power density at each spatial grid point For the first Unit volume at each spatial grid point Air density is used to characterize the abundance of wind resources. If it is necessary to analyze relevant indicators, the ratio of wind speed variance to mean is calculated in a local neighborhood or time dimension to obtain an approximate estimate of turbulence intensity I, which is used for wind turbine fatigue load and comfort assessment. Relevant indicators include turbulence intensity. Step 5.5: Based on the physical constraints introduced during the training phase, perform a post-hoc physical consistency check on the predicted wind field. For example, this can be done on any spatial grid point during the prediction phase. Calculate the numerical divergence:
[0079] in, To predict wind field at spatial grid points The divergence value can be used to evaluate whether the prediction results satisfy the incompressibility condition; Spatial grid points One of the coordinate components; By statistically analyzing the divergence distribution across the entire grid corresponding to the new target complex terrain region, it is determined whether there are physically inconsistent regions in the PINN model's predictions. If no physically inconsistent regions exist, the physical test passes, and the predicted wind field and its derived indices can be used in relevant engineering scenarios. These scenarios include wind power site selection, urban ventilation corridor planning, or building wind load analysis. For example, in wind power applications... The spatial distribution selects high-wind-energy-density areas as candidate sites, and in urban planning, it is based on... By identifying well-ventilated or poorly ventilated areas using streamlined structures, the predictive results of this application can be directly transformed into actionable engineering decision-making basis.
[0080] This application implements a fast prediction method for wind fields in 3D complex terrain that integrates terrain coding, environment-driven, similar scene transfer and physical constraint neural networks, enabling wind field prediction to have high accuracy, strong generalization, high physical consistency and fast computation capability.
[0081] It should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of this application. Any modifications or equivalent substitutions that do not depart from the spirit and scope of this application should be covered within the protection scope of the claims of this application.
Claims
1. A method for predicting wind fields in three-dimensional complex terrain, characterized in that, include: Step 1: Obtain the elevation matrix by processing the Digital Elevation Model (DEM) corresponding to the complex terrain of the target area, and then... ， The gradient and slope of the terrain are obtained, and the terrain feature vector corresponding to the complex terrain of the target is obtained based on the gradient and slope of the terrain. Step 2: Obtain a set of similar wind field data based on the terrain feature vectors corresponding to the complex terrain of the target; Step 3: Obtain the prior wind field based on the similar wind field data set; Step 4: Input the terrain feature vector and prior wind field into the Physically Constrained Neural Network (PINN) to obtain the three-dimensional wind speed. Based on the three-dimensional wind speed, obtain the total loss of the Physically Constrained Neural Network (PINN). By minimizing the total loss, obtain the trained PINN model. Step 5: Construct a three-dimensional computational domain within the new target complex terrain area, and divide the three-dimensional computational domain into several sets of spatial grid points to be predicted. Input each spatial grid point in the set of spatial grid points, its corresponding terrain feature vector, and the prior wind field into the trained PINN model to obtain the three-dimensional wind speed corresponding to each spatial grid point, and finally obtain the wind field of the new target complex terrain area.
2. The method according to claim 1, characterized in that, Step 1 includes: Step 11: Calculate the gradient of the elevation matrix H in the x and y directions: ， in, S x and S y The x and y axes represent the east-west and north-south gradients, respectively. The origin of the global unified spatial coordinate system is the reference starting point of the terrain data in the horizontal projection plane, that is, a boundary corner point within the horizontal projection range of the terrain. The x-axis represents the east-west direction of the terrain, the y-axis represents the north-south direction of the terrain, and the z-axis represents the height of the terrain. The slope is obtained from the gradient using the following formula: Here, slope indicates the degree of local terrain slope; Step 12: Obtain the surface roughness intensity based on the elevation matrix H; Step 13: Obtain the TRI index based on the elevation value of the grid point to be evaluated and the elevation values of its neighboring grid points; Step 14: Based on the surface roughness intensity, slope, surface roughness intensity, and TRI index, obtain the terrain feature vector corresponding to the target complex terrain.
3. The method according to claim 2, characterized in that, Step 12 includes: The surface roughness intensity is obtained using an empirical formula based on the standard deviation of elevation. : Among them, std( H ) represents the standard deviation of the elevation matrix; Step 13 includes: Surface classification data is converted into one-hot encoding to distinguish surface types; surface types include water bodies, vegetation, bare land, and built-up areas; surface classification data includes surface type information obtained through remote sensing imagery, topographic surveys, or other geographic information systems (GIS); The TRI index, used to describe the intensity of terrain undulation, is obtained through the following formula: in, () represents the elevation value of the grid point to be evaluated. express Within the neighborhood The elevation values of each grid point are given, where M is the total number of grid points in the neighborhood participating in the calculation. Step 14 includes: The terrain feature vector is obtained using the following formula: Where T is the terrain feature vector corresponding to the target complex terrain, and one-hot is the one-hot encoding of the land surface type.
4. The method according to claim 1, characterized in that, Step 2 includes: Step 21: Combine the feature vectors of multiple terrain regions The corresponding wind field data Paired storage is performed to form a terrain-wind field sample library; Step 22: Based on the Euclidean distance between the terrain feature vector corresponding to the target complex terrain and the feature vector in the terrain-wind field sample library, select a preset number of terrain regions from the terrain-wind field sample library, and construct a similar wind field data set by combining the wind field data corresponding to the preset number of terrain regions.
5. The method according to claim 4, characterized in that, Step 3 includes: Step 31: In wind field prediction, an environmental feature vector is constructed based on environmental factors, including incoming wind speed, incoming wind direction, atmospheric stability, and surface temperature. Step 32: Convert the environmental feature vector into response values for similar wind fields using the weighted generation network (WGN); Step 33: Obtain the corresponding weights based on the response values of similar wind fields; Step 34: Based on the weights and the corresponding wind field data in the similar wind field dataset, obtain the prior wind field obtained under the combined effect of the terrain feature vector and the environmental feature vector corresponding to the target complex terrain.
6. The method according to claim 5, characterized in that, Step 32 includes: The response values for similar wind fields can be obtained using the following formula: in, Represents the first element in a set of similar wind field data under environmental conditions. The response level of a wind field, where k represents the total number of similar wind field data in the similar wind field dataset; Step 33 includes: Use Softmax to generate normalized weights: in, This represents the normalized weight of the i-th wind field in the similar wind field dataset under the current environmental conditions. Represents the first element in a set of similar wind field data under environmental conditions. The degree of response to similar wind fields; Step 34 includes: The prior wind field is obtained using the following formula: in, The weights represent the prior wind field obtained under the combined influence of terrain feature vector T and environmental feature vector E. Indicates the effect of environmental conditions on the first The adjustment coefficient of each wind field.
7. The method according to claim 1, characterized in that, Step 4 includes: Step 41: Input the terrain feature vector and prior wind field into the Physically Constrained Neural Network (PINN) to obtain the three-dimensional wind speed; Step 42: Based on the prior wind field and the actual wind field, obtain the data error term; Step 43: Based on the three-dimensional wind speed, obtain the continuity loss and momentum residual; Step 44: Obtain the momentum loss based on the momentum residual; Step 45: Obtain the total loss based on the data error term, continuity loss, and momentum loss; Step 46: By minimizing the total loss, the trained PINN model is obtained.
8. The method according to claim 7, characterized in that, Step 42 includes: The data error term is obtained using the following formula: in, This represents the data error term, used to measure the model's prediction of the prior wind field. With real wind field The differences between them; Step 43 includes: The continuous loss is obtained using the following formula. : in, Indicates the divergence of the wind field. Approaching zero to ensure that the predicted wind field satisfies the continuity condition of incompressible flow; This represents the wind speed component in one dimension of a three-dimensional wind speed. The gradient operator with respect to spatial coordinates is used to describe the rate of change of a physical quantity in space; The momentum residual is obtained using the following formula. for: in, The pressure scalar field representing the pressure field in the wind field is the pressure term in the momentum equation of an incompressible fluid; air density, For dynamic viscosity, For volume forces, This indicates the degree of deviation of the momentum equation from the current predicted wind field, and is used to measure whether the output of the PINN model satisfies the momentum conservation equation for incompressible fluids. This represents the convection term, describing the spatial variation of fluid velocity as it moves. The Laplace operator is used to describe momentum diffusion; Step 44 includes: The momentum loss is obtained using the following formula: in, Indicates momentum loss; Step 45 includes: The total loss is obtained using the following formula: in, For the total loss, These are the weighting coefficients.
9. The method according to claim 1, characterized in that, Step 5 includes: Step 51: Construct a 3D computational domain within the new target complex terrain region. and in the three-dimensional computational domain The space is divided into several sets G of spatial grid points to be predicted according to the given horizontal and vertical resolution: in, Indicates the first There are N spatial grid points, where N is the total number of grid points in each set G. The three-dimensional spatial extent of the new target complex terrain region; For a globally unified spatial coordinate system The three coordinate components; Step 52: Combine each spatial grid point in the spatial grid point set G with the corresponding terrain feature vector and prior wind field information to form the input vector of the Physically Constrained Neural Network (PINN); Let the first... The input of the grid points is : in, For the first The input vector of spatial grid points, Indicates at spatial grid points The surrounding local terrain feature vector is obtained by encoding the terrain feature vector. This indicates that the prior wind field obtained by weighting environmental feature vectors is represented at spatial grid points. Interpolated value or nearest neighbor value at the location; Physically constrained neural networks (PINN) are considered as having parameters. The nonlinear mapping function will... Input of spatial grid points The mapping is to a three-dimensional wind speed output, which takes the following form: in, For a well-trained PINN model, For the PINN model at spatial grid points The predicted three-dimensional wind speed vector is obtained at that location. These are the wind speed components of the three-dimensional wind speed vector in three directions; By all By performing forward reasoning, the predicted wind field for the entire new target complex terrain area can be obtained in one go.
10. The method according to claim 9, characterized in that, After step 5, the following is also included: vector set All or part of Composition matrix And calculate the set of wind speed vectors obtained by performing one or more forward inference operations. : in, In the three-dimensional computational domain The set of predicted wind speed vectors at all spatial grid points is considered to be of size . The matrix, Each row of the matrix corresponds to the three-dimensional wind speed of a spatial grid point; Will Remapping back to the spatial coordinate system, construct a discrete wind field function defined on Ω. If you need to adjust any position in the spatial coordinate system Interpolation will then determine the discrete wind speed. Convert to continuous field function This makes the wind field more smooth and continuous in visualization and post-processing analysis; Obtaining the three-dimensional wind speed vector Then, calculate the wind speed amplitude: in, For the first The wind speed at each spatial grid point is used for wind energy density and wind environment assessment. , , Representing discrete wind speeds The three components; For wind energy applications, calculate the wind power density per unit volume: in, For the first Wind power density at each spatial grid point For the first Unit volume at each spatial grid point Air density is used to characterize the abundance of wind resources. If it is necessary to analyze relevant indicators, the ratio of wind speed variance to mean is calculated in a local neighborhood or time dimension to obtain an approximate estimate of turbulence intensity, which is used for wind turbine fatigue load and comfort assessment. Relevant indicators include turbulence intensity. Step 5.5: For arbitrary spatial grid points in the prediction phase Calculate the numerical divergence: in, To predict wind field at spatial grid points The divergence value is used to evaluate whether the prediction results satisfy the incompressibility condition; Spatial grid points One of the coordinate components; By statistically analyzing the divergence distribution across the entire grid corresponding to the new target complex terrain area, it is determined whether there are physically inconsistent regions in the prediction of the PINN model. If there are no physically inconsistent regions, the physical test is passed, and the predicted wind field and its derived indices can be used in relevant engineering scenarios. Relevant engineering scenarios include wind energy site selection, urban ventilation corridor planning, or building wind load analysis.