A neutral mesh-based ship free-surface wave form prediction method
By using a neutral grid-based method, the free surface elevation field at different speeds is mapped onto the same spatial reference frame, solving the problem of inconsistent free surface waveform distribution in traditional CFD calculations. This enables fast and stable prediction of waveforms across speeds, improving the model's prediction accuracy and reliability.
Patent Information
- Application Number
- CN202610722100.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-05-25
- Publication Date
- 2026-08-25
AI Technical Summary
In ship hydrodynamics research, traditional CFD calculation methods suffer from inconsistent free surface waveform distributions under different operating conditions due to the differences in flow field characteristics at different speeds. This makes it difficult to compare and perform data-driven modeling within a unified framework, limiting the generalization ability of prediction models and introducing systematic errors, thus reducing the reliability and application value of prediction results.
A neutral grid-based method is adopted to generate a two-dimensional neutral grid that is independent of the flight speed. The free surface elevation field at different flight speeds is mapped to the same spatial reference frame. By constructing a waveform prediction model and training it with a composite loss function, the stability and consistency of the model under cross-flight speed conditions are ensured.
It achieves rapid and stable prediction of free-plane waveforms across speeds, avoids distribution offset and error drift, ensures the comparability and consistency of prediction results, is applicable to ship design and performance evaluation, reduces computational costs and improves the engineering credibility of the model.
Smart Images
Figure CN122634741A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of ship hydrodynamics, and in particular to a method for predicting ship free surface waveforms based on neutral grids. Background Technology
[0002] In ship hydrodynamics research, the free-plane waveform of a ship during navigation is an important indicator for evaluating navigation performance, wave resistance, and wake characteristics. In recent years, with the rapid development of computational fluid dynamics (CFD) methods, researchers have been able to obtain the ship's free-plane waveform under different speed conditions with relatively high accuracy through numerical means.
[0003] However, due to the significant differences in flow field characteristics at different speeds, CFD calculations often require the design of differentiated mesh topologies and refinement strategies for each speed to ensure computational convergence and interface capture accuracy. This results in free surface waveforms obtained under different operating conditions not only being distributed across different spatial coordinate ranges but also corresponding to different mesh resolutions and node topologies, making it difficult to compare and perform data-driven modeling within a unified framework.
[0004] Traditional processing methods typically use the original CFD grid or sparse experimental measurement points for interpolation and resampling, which can easily lead to inconsistencies in the spatial representation of training data across different operating conditions, limiting the generalization ability of the prediction model under unknown operating conditions. Furthermore, during the model training and inference phases, the use of different grid spatial distribution strategies often introduces systematic errors, reducing the engineering reliability and application value of the prediction results. Summary of the Invention
[0005] To address the aforementioned problems and technical requirements, this application proposes a method for predicting the free surface waveform of a ship based on a neutral grid. The technical solution of this application is as follows: A method for predicting the free surface waveform of a ship based on a neutral grid, the method comprising: Numerical simulations were conducted on ships under the same draft T and different sample speeds, and a sample set was constructed. Each sample in the sample set is the steady-state free surface elevation field of the ship at the corresponding sample speed. Based on the maximum sample speed during the numerical simulation process Determine the grid step size, and generate a two-dimensional neutral grid independent of the flight speed according to the grid step size. The two-dimensional neutral grid is located in... The plane is parallel to the horizontal plane; Projecting the steady-state free surface elevation field of each sample onto a two-dimensional neutral grid yields the labeled elevations at each two-dimensional neutral grid point within the free surface region. ; The sample input features are constructed based on the sample velocity and the grid coordinates of each two-dimensional neutral grid within the free surface area for each sample. These features are then input into a pre-built waveform prediction model to obtain the predicted elevation at each two-dimensional neutral grid within the free surface area. Based on the marked elevations at each two-dimensional neutral grid point within the free surface area. and predicted elevation Calculate the loss function and train the waveform prediction model; Based on the target speed of the ship at draft T and the grid coordinates of each two-dimensional neutral grid in the free surface region, the features to be predicted are constructed and input into the trained waveform prediction model to obtain the free surface waveform prediction results of the ship at draft T and target speed.
[0006] A further technical solution involves using the maximum sample speed from the numerical simulation process. Determining the grid step size includes: Based on the maximum sample speed Calculate the shortest target wavelength , It is the acceleration due to gravity; Determine the longitudinal step size of the grid along the ship's length. And determine the lateral step size of the grid along the ship's width direction. Among them, parameters ,parameter .
[0007] A further technical solution involves generating a two-dimensional neutral grid independent of flight speed according to the grid step size, including: A two-dimensional neutral grid, independent of speed, is generated within the ship's preset outward range according to the grid step size. The preset outward range covers the bow wave initiation disturbance area and provides boundary buffer in the longitudinal forward direction of the ship, accommodates the main wave train, multiple major peak and valley periods and their initial attenuation process in the longitudinal rearward direction of the ship, and covers the main influence area of the Kelvin wedge wave system on both sides of the ship in the transverse direction.
[0008] A further technical solution is that the preset outward range of the vessel covers a longitudinal area along its length, including... The lateral coverage along the width of the ship includes ;in, It is the vertical length of the ship.
[0009] The further technical solution is that the waveform prediction model is constructed based on an MGN network. The sample input features are constructed according to the sample velocity of each sample and the grid coordinates of each two-dimensional neutral grid within the free surface region, including: The grid coordinates of each two-dimensional neutral grid within the free surface region. Dimensional consistency processing is performed to obtain ;in, It is the vertical length of the ship; The elevations at each two-dimensional neutral grid point are calculated using the discrete differential geometry of the two-dimensional neutral grid within the free surface region. Geometric prior features; Determine any two-dimensional neutral grid within the free surface region. and two-dimensional neutral mesh Length of the connecting edge Normalized direction vector and local elevation differences This constitutes a local edge feature; among which, It is a two-dimensional neutral mesh Grid coordinates, It is a two-dimensional neutral mesh Grid coordinates, It is a two-dimensional neutral mesh The marked elevation, It is a two-dimensional neutral mesh Mark the elevation; Combined with the sample speed Dimensionally consistent grid coordinates The sample input features are obtained from geometric prior features and local edge features.
[0010] A further technical solution involves projecting the steady-state free surface elevation field of each sample onto a two-dimensional neutral grid to obtain the labeled elevations at each two-dimensional neutral grid within the free surface region. include: Projecting the steady-state free surface elevation field of each sample onto a two-dimensional neutral grid yields the labeled elevations at multiple scattered points. The minimum convex polygon is determined based on scattered points as the effective interpolation region. The labeled elevations at each two-dimensional neutral grid within the free surface region of the effective interpolation region are obtained using Delaunay barycentric linear interpolation. The labeled elevations at each two-dimensional neutral grid outside the effective interpolation region are obtained using the radial basis function (RBF). .
[0011] A further technical solution is that the ship free surface waveform prediction method also includes: A mask is generated based on the ship's waterline projection at draft T. The two-dimensional neutral grid outside the mask area is determined to belong to the two-dimensional neutral grid within the free surface area. The elevations of the two-dimensional neutral grid points within the mask area are then labeled. The value is assigned to NaN, or the weights of the two-dimensional neutral grid located within the mask are reset to 0 when training the waveform prediction model.
[0012] A further technical solution involves using the marked elevations at various two-dimensional neutral grid points within the free surface area. and predicted elevation The loss function is calculated as follows: Based on the marked elevations at each two-dimensional neutral grid point within the free surface area and predicted elevation Calculate elevation prediction loss ;in, It is the number of two-dimensional neutral grids within the free surface region. It is a set of two-dimensional neutral grids within the free surface region. Represents any two-dimensional neutral grid within the free surface region. The elevation marking at that location, Represents any two-dimensional neutral grid within the free surface region. Predicted elevation at the location; Based on the marked elevations at each two-dimensional neutral grid point within the free surface area and predicted elevation The uniformity in local slope and curvature yields the gradient curvature uniformity regularization term. ; Based on the marked elevations at each two-dimensional neutral grid point within the free surface area and predicted elevation The uniformity in dominant wavelength and wavenumber energy distribution yields a lightweight spectral uniformity regularization term. ; Calculate the loss function , and These are the coefficients of two regularization terms.
[0013] Its further technical solution is a gradient curvature consistency regularization term. The calculation formula is:
[0014] in, Indicates elevation marking In a two-dimensional neutral grid gradient at, Indicates elevation marking In a two-dimensional neutral grid Along The first derivative of the direction, Indicates elevation marking In a two-dimensional neutral grid Along The first derivative in the direction; Indicates predicted elevation In a two-dimensional neutral grid gradient at, Indicates predicted elevation In a two-dimensional neutral grid Along The first derivative of the direction, Indicates predicted elevation In a two-dimensional neutral grid Along The first derivative in the direction; This indicates the calculation of the L2 norm; Represents the coefficient of the regularization term; Indicates elevation marking In a two-dimensional neutral grid The average curvature at that point and , Indicates elevation marking In a two-dimensional neutral grid Along The second derivative of the direction, Indicates elevation marking In a two-dimensional neutral grid Along The second derivative of the direction; Indicates predicted elevation In a two-dimensional neutral grid The average curvature at that point and , Indicates predicted elevation In a two-dimensional neutral grid Along The second derivative of the direction, Indicates predicted elevation In a two-dimensional neutral grid Along The second derivative in the direction.
[0015] A further technical solution involves calculating a lightweight spectral consistency regularization term. include: Label the elevation at each two-dimensional neutral grid point within the free surface region. After removing the mean and windowing, a two-dimensional Fourier transform is performed to obtain the normalized spatial wavenumber spectrum energy distribution. ; Predicted elevations at each two-dimensional neutral grid point within the free surface region After removing the mean and windowing, a two-dimensional Fourier transform is performed to obtain the normalized spatial wavenumber spectrum energy distribution. ; Based on the energy distribution of the normalized spatial wavenumber spectrum and normalized spatial wavenumber spectrum energy distribution Calculate the lightweight spectral consistency regularization term using the following formula. :
[0016] in, For discrete wavenumber bandwidth determined based on the dominant wavelength, It is a two-dimensional space wavenumber pair.
[0017] The beneficial technical effects of this application are: This application discloses a ship free surface waveform prediction method based on a neutral grid. This method establishes a speed-independent two-dimensional neutral grid as the same spatial reference system and topology, and maps the steady-state free surface elevation field at different speeds onto the same spatial reference system and topology for model training. The same two-dimensional neutral grid is also used during model inference. This method solves the data inconsistency problem caused by the change of traditional CFD grid with different operating conditions, and realizes fast and stable prediction of free surface waveforms across speeds. It avoids distribution offset and error drift in cross-operating condition prediction. This method can achieve consistent alignment and fast prediction of waveform data at different speeds with a specific draft, enabling the model to directly output the steady-state three-dimensional free surface under unknown draft and unknown speed, while maintaining physical consistency in spectral and geometric features, ensuring the comparability and consistency of prediction results. It is applicable to ship design, performance evaluation and virtual simulation scenarios.
[0018] This method uniformly calculates geometric prior features on a two-dimensional neutral mesh triangulation and uses them as input features for samples. Combined with a composite loss function including two physical consistency regularization terms, the waveform prediction model maintains smoothness without excessive smoothing. The geometric structures of the Kelvin wedge angle, dominant wavelength, and stern wave train remain accurate even at unknown speeds. Furthermore, free surfaces exhibit multi-valued or near-multi-valued topologies in regions such as stern flow, rewind, and breakup. Direct regression using triangulation elevations often leads to gradient explosion, local oscillations, and training instability. This method uses the PositionZ single-valued aperture and flattens the breakup / rewind regions, reducing the multi-valued or near-multi-valued geometric problems to a single scalar function approximation. The training process is no longer plagued by local backsliding and spikes, exhibiting stable and repeatable convergence behavior numerically.
[0019] The waveform prediction model in this application does not depend on additional parameters such as the Froude number or principal scale ratio, facilitating its application across different solvers and ship types and scales. Furthermore, it is not tied to a specific solver or file format, allowing for seamless migration across various CFD sources such as STAR-CCM+. This method utilizes the trained waveform prediction model to reduce the computational cost of reconstructing steady-state free surfaces across operating conditions from minutes / hours in traditional CFD to seconds, achieving an order-of-magnitude speedup, while avoiding error accumulation and pipeline complexity caused by repeated resampling between meshes. Attached Figure Description
[0020] Figure 1 This is a flowchart illustrating a method for predicting the free surface waveform of a ship according to an embodiment of this application.
[0021] Figure 2 This is a schematic diagram of a two-dimensional neutral grid generated within a preset outward range of a ship in an example, and a schematic diagram of projecting the steady-state free surface elevation field of a sample onto the two-dimensional neutral grid. Detailed Implementation
[0022] The specific embodiments of this application will be further described below with reference to the accompanying drawings.
[0023] This application discloses a ship free surface waveform prediction method based on neutral grids, applicable to multi-speed conditions under specific draft conditions. The method includes the following steps; please refer to [reference needed]. Figure 1 The flowchart shown: Step 1: Conduct numerical simulations of the ship under the same draft T and different sample speeds and construct a sample set. Each sample in the sample set is the steady-state free surface elevation field of the ship at the corresponding sample speed.
[0024] This step, when constructing the sample set, is not limited to a specific solver in terms of data source; it only requires the ability to derive the steady-state free surface elevation field of the PositionZ scalar. In CAE software such as STAR-CCM+, .case / .geo files and free surface elevation files can be directly read, or a steady-state free surface elevation field equivalent to PositionZ can be obtained by converting the VOF isosurface to elevation at 0.5.
[0025] Step 2, based on the maximum sample speed during the numerical simulation process. Determine the grid step size.
[0026] First, based on the maximum sample speed Calculate the shortest target wavelength :
[0027] in, This is the acceleration due to gravity.
[0028] Then based on the shortest target wavelength The mesh step size is determined; that is, the mesh step size of the two-dimensional neutral mesh generated in this application is not a fixed constant, but is based on the shortest target wavelength. The required sampling resolution is determined. This step involves determining the grid step size along the ship's length. Grid vertical step size and along the width of the ship Horizontal step size of the grid :
[0029]
[0030] Among them, parameters To ensure the calculated vertical step size of the grid Satisfy the peak and trough localization and spectral resolution of the main wave train in the bow-stern direction. Parameters So that the calculated lateral step size of the mesh is... Ensure the geometric shape of the oblique ridge within the Kelvin angular zone is preserved.
[0031] This application allows for a vertical grid step size. and grid horizontal step size They are not equal, and the vertical sampling density is usually higher than the horizontal sampling density, therefore The value is slightly greater than This makes the vertical step size of the grid... Smaller than the horizontal step size of the grid In one embodiment, take , .
[0032] Step 3: Then, generate a two-dimensional neutral grid independent of the flight speed according to the grid step size determined in Step 2. The generated two-dimensional neutral grid is located in... The plane is parallel to the horizontal plane.
[0033] According to the grid step size , When generating a speed-independent 2D neutral mesh, it is generated within a preset outrigger range of the ship. The preset outrigger range is along the ship's length. The coverage area is In the direction of ship width The coverage area is Then, within the preset outward range, the data generated along the ship's length direction... Number of grids Along the width of the ship Number of grids ,in, Indicates rounding down. Located along the length of the ship. The Individual, ship width direction The The two-dimensional neutral grid at each location is denoted as the two-dimensional neutral grid. 2D neutral mesh The grid coordinates are written as And in the captain's direction coordinates In the direction of the ship's width coordinates Integer parameters Integer parameters .
[0034] The preset outreach range of the ship is not arbitrarily set, but is determined comprehensively based on the main spatial distribution characteristics of the ship's traveling waves and the computational scale of the two-dimensional neutral grid. The preset outreach range of the ship has a rectangular structure, and the coverage requirements are as follows: In the longitudinal forward direction, it covers the initial disturbance area of the bow wave and provides a boundary buffer for interpolation extrapolation. In the longitudinal aft direction, it accommodates the main wave train aft, multiple main peak-valley periods, and their initial attenuation processes to ensure that the free spectrum characteristics and peak-valley morphology are not distorted due to domain truncation. Laterally, it covers the main influence areas of the Kelvin wedge wave system on both sides of the ship to avoid the wave angle structure being clipped due to excessively close lateral boundaries.
[0035] The aforementioned preset outreach range ensures the complete preservation of key geometric features of the ship's waves while controlling the number of two-dimensional neutral grids and the scale of the graph structure, representing a trade-off between physical coverage and computational efficiency. Based on meeting the above coverage requirements, the preset outreach range of the ship can also be equivalently adjusted according to the ship's dimensions, design speed range, and target fidelity requirements.
[0036] Based on the aforementioned coverage requirements, in one embodiment, determining the vessel's preset outward range includes: along the length of the vessel. The longitudinal coverage includes Along the width of the ship The horizontal coverage area includes .in, It is the vertical length of the ship.
[0037] For example, in one instance, step 1 involves conducting numerical simulations at a draft of T = 0.5m and 29 different sample speeds {10, 10.5, 11, 11.5, 12, 12.5, 13, 13.5, 14, 14.5, 15, 15.5, 16, 16.5, 17, 17.5, 18, 18.5, 19, 19.5, 20, 20.5, 21, 21.5, 22, 22.5, 23, 23.5, 24} to construct a sample set. The numerical unit of the sample speeds is knots (kn). The maximum sample speed during the numerical simulation is... If the wavelength is 24kΩ, then the shortest target wavelength can be calculated. It is 97.64 m / s. In , The vertical step size of the grid can be calculated under these conditions. Horizontal step size of the grid .
[0038] vertical length of ship The pre-defined outward range of the vessel includes as well as Within the preset extension range, the grid is adjusted according to the vertical step size. Horizontal step size of the grid Generate along the ship's length direction of A two-dimensional neutral grid, and along the ship's width direction of Two-dimensional neutral grids, containing a total of A two-dimensional neutral grid.
[0039] Step 4: Project the steady-state free surface elevation field of each sample onto a two-dimensional neutral grid to obtain the labeled elevations at each two-dimensional neutral grid within the free surface region. The labeled elevation at each two-dimensional neutral grid. This represents the actual engineering elevation at the location of the two-dimensional neutral grid, or the relative elevation between the actual engineering elevation at the location of the two-dimensional neutral grid and the plane containing the two-dimensional neutral grid, to enhance numerical discriminability.
[0040] This step first projects the steady-state free surface elevation field of each sample onto a two-dimensional neutral grid to obtain the labeled elevations at multiple scattered points. Then, the smallest convex polygon is determined as the effective interpolation region based on the scattered points.
[0041] Within the effective interpolation region, the labeled elevations at each two-dimensional neutral grid within the free surface region of the effective interpolation region are obtained using Delaunay centroid linear interpolation. .
[0042] Within the pre-defined outreach range of the ship, excluding the effective interpolation region, the labeled elevations at each two-dimensional neutral grid outside the effective interpolation region are obtained using the radial basis function (RBF). This achieves a smooth outward extension.
[0043] While generating a 2D neutral mesh, a mask is also generated based on the ship's waterline projection at draft T. This mask determines that 2D neutral meshes outside the mask area belong to the 2D neutral meshes within the free surface area, and that 2D neutral meshes within the mask area are located inside the hull and are removed, thus ensuring that the dataset is aligned within a consistent physical domain. When removing 2D neutral meshes within the mask area, the labeled elevations at the 2D neutral mesh locations within the mask area can be... The value is assigned to NaN, or the weights of the two-dimensional neutral grid located within the mask are reset to 0 when training the waveform prediction model later.
[0044] For example, in one instance, such as Figure 2 As shown, a horizontal coordinate system is established with the projected position of the bow of the ship as the origin. This horizontal coordinate system... The direction is along the length of the ship, with the direction pointing towards the stern as positive. This horizontal coordinate system... The direction is along the width of the ship, with the direction pointing to the starboard side being the positive direction. Figure 2 The dashed box represents the effective interpolation region determined by the scatter points, and the white area is a mask generated based on the ship's hull waterline projection at draft T. The two-dimensional neutral grid within this mask is removed.
[0045] Step 5: Construct sample input features based on the sample velocity of each sample and the grid coordinates of each two-dimensional neutral grid within the free surface area. Input these features into the pre-built waveform prediction model to obtain the predicted elevation at each two-dimensional neutral grid within the free surface area. Based on the marked elevations at each two-dimensional neutral grid point within the free surface area. and predicted elevation Calculate the loss function and train the waveform prediction model.
[0046] In one embodiment, the waveform prediction model is constructed based on an MGN (Mesh Graph Net) network, which includes an encoder, a processor, and a decoder. The encoder uses a multilayer perceptron to map low-dimensional sample input features to the latent space. The processor employs a multilayer message-passing neural network (MPNN), where each layer first performs weighted aggregation of the latent representations of adjacent grids based on edge features, and then uses "sum" aggregation to ensure symmetry and numerical stability. The activation function uses LeakyReLU to mitigate gradient vanishing. The decoder restores the grid latent representations to the target scalar field.
[0047] The sample input features of the waveform prediction model include operating parameters, grid coordinates, and local edge features: (1) The operating parameters are the sample speeds corresponding to this sample. .
[0048] (2) To avoid the influence of numerical differences in different numerical simulations, the grid coordinates of each two-dimensional neutral grid in the free liquid surface region are set. After dimension-unified processing, the coordinates are based on the dimension-unified grid. As input, It is the vertical length of the ship.
[0049] (3) Local edge features, including: arbitrary two-dimensional neutral grid and two-dimensional neutral mesh Length of the connecting edge Normalized direction vector and local elevation differences .in, It is a two-dimensional neutral mesh Grid coordinates, It is a two-dimensional neutral mesh Grid coordinates, It is a two-dimensional neutral mesh The marked elevation, It is a two-dimensional neutral mesh The elevation is marked. Side length. Through a two-dimensional neutral grid and two-dimensional neutral mesh The grid coordinates can be calculated from them.
[0050] One approach is to combine the sample flight speed with the sample data. Dimensionally consistent grid coordinates The sample input features are obtained by combining local edge features and written as follows: .
[0051] In another embodiment, the discrete differential geometry of each two-dimensional neutral grid within the free surface region is further calculated to determine the marked elevation at each two-dimensional neutral grid. Geometric prior features are used to enhance node features. Elevation is labeled at each calculated 2D neutral grid. The geometric prior features include at least one of the following categories of geometric prior features: (a) Annotated elevations at each two-dimensional neutral grid Along First derivative of direction In one embodiment, a two-dimensional neutral grid is obtained by uniform difference calculation on the two-dimensional neutral grid. Along First derivative of direction :
[0052] (b) Annotated elevations at each two-dimensional neutral grid Along First derivative of direction In one embodiment, a two-dimensional neutral grid is obtained by uniform difference calculation on the two-dimensional neutral grid. Along First derivative of direction :
[0053] (c) Labeled elevations at each two-dimensional neutral grid Along Second derivative of direction In one embodiment, a two-dimensional neutral grid is obtained by uniform difference calculation on the two-dimensional neutral grid. Along Second derivative of direction :
[0054] (d) Labeled elevations at each two-dimensional neutral grid Along Second derivative of direction In one embodiment, a two-dimensional neutral grid is obtained by uniform difference calculation on the two-dimensional neutral grid. Along Second derivative of direction :
[0055] (e) Annotated elevations at each two-dimensional neutral grid Along Second derivative of direction In one embodiment, a two-dimensional neutral grid is obtained by uniform difference calculation on the two-dimensional neutral grid. Along Second derivative of direction :
[0056] (f) Labeled elevations at each two-dimensional neutral grid average curvature Two-dimensional neutral mesh mean curvature .
[0057] (g) Unit normal at each two-dimensional neutral grid Under the assumption of small slope, a two-dimensional neutral grid Unit normal direction .
[0058] Then in the sample speed Dimensionally consistent grid coordinates Based on local edge features, geometric prior features are further combined to obtain sample input features. For example, when the combined geometric prior features include the first derivative... First derivative Mean curvature When the sample input features are obtained, they are written as: .
[0059] To further stabilize convergence and suppress excessive smoothing, a composite loss function is used in one embodiment. ,include: (1) Elevation prediction loss
[0060] This loss is the most basic MSE principal loss, which includes the labeled elevations at each two-dimensional neutral grid point within the free surface region. and predicted elevation Calculate elevation prediction loss :
[0061] in, It represents the number of two-dimensional neutral grids within the free surface region. It is a set of two-dimensional neutral grids within the free surface region. Represents any two-dimensional neutral grid within the free surface region. The elevation marking at that location, Represents any two-dimensional neutral grid within the free surface region. Predicted elevation at the location.
[0062] (2) Gradient curvature consistency regularization term
[0063] The gradient curvature consistency regularization term Based on the marked elevations at each two-dimensional neutral grid point within the free surface area and predicted elevation The consistency in local slope and curvature is obtained, and the calculation formula is as follows:
[0064] in, This indicates the calculation of the L2 norm. This represents the coefficient of the regularization term.
[0065] Indicates elevation marking In a two-dimensional neutral grid The gradient at that point. Indicates elevation marking In a two-dimensional neutral grid Along The first derivative of the direction, Indicates elevation marking In a two-dimensional neutral grid Along The first derivative in the direction. and The calculation formula is as above.
[0066] Indicates predicted elevation In a two-dimensional neutral grid The gradient at that point. Indicates predicted elevation In a two-dimensional neutral grid Along The first derivative of the direction, Indicates predicted elevation In a two-dimensional neutral grid Along The first derivative in the direction. Similarly, it is calculated using uniform difference on a two-dimensional neutral grid. and :
[0067]
[0068] Indicates elevation marking In a two-dimensional neutral grid The average curvature at that point and , Indicates elevation marking In a two-dimensional neutral grid Along The second derivative of the direction, Indicates elevation marking In a two-dimensional neutral grid Along The second derivative in the direction. To and The calculation formula is as above.
[0069] Indicates predicted elevation In a two-dimensional neutral grid The average curvature at that point and , Indicates predicted elevation In a two-dimensional neutral grid Along The second derivative of the direction, Indicates predicted elevation In a two-dimensional neutral grid Along The second derivative of the direction is similarly obtained by uniform difference calculation on a two-dimensional neutral grid. and :
[0070]
[0071] (3) Lightweight spectral uniformity regularization term
[0072] The lightweight spectral consistency regularization term Based on the marked elevations at each two-dimensional neutral grid point within the free surface area and predicted elevation The consistency calculation based on the dominant wavelength and wavenumber energy distribution is obtained, and the calculation formula is as follows:
[0073] in, The elevation markings at each two-dimensional neutral grid point within the free surface area. The normalized spatial wavenumber spectrum energy distribution is obtained by performing a two-dimensional Fourier transform after removing the mean and adding a window.
[0074] Predicted elevations at various two-dimensional neutral grid points within the free surface region. The normalized spatial wavenumber spectrum energy distribution is obtained by performing a two-dimensional Fourier transform after removing the mean and adding a window.
[0075] To determine the discrete wavenumber bandwidth based on the dominant wavelength, one embodiment selects the low-to-medium wavenumber region near the dominant wavelength as the discrete wavenumber bandwidth. . Discrete wavenumber bandwidth Two-dimensional space wavenumber pairs in the .
[0076] Loss Prediction Based on Elevation Based on this, two physical consistency regularization terms are superimposed to obtain the composite loss function in this embodiment. :
[0077] in, and These are the coefficients of two regularization terms.
[0078] Through this loss function The waveform prediction model is constrained by local slope, local curvature and dominant wavelength structure while predicting elevation at the fitting two-dimensional neutral grid. This reduces waveform over-smoothing, local oscillation and main wave train misalignment problems, which is beneficial to improving the stability and morphological fidelity of three-dimensional steady-state free surface prediction under unknown speed conditions.
[0079] In the iterative optimization of the waveform prediction model, feature normalization, weight decay, and gradient clipping are employed, and exponential moving averages are used to smooth the parameters to prevent high-frequency noise from being amplified at higher-order differences. The model structure and computing power configuration follow the principles of "reproducibility and transferability." In one instance, a 12-15 layer message-passing neural network is used with a hidden channel width of approximately 256. "sum" aggregation and LeakyReLU are employed, and batch normalization or layer normalization is interspersed between the encoder and processor to stabilize training. Since the sample input features only contain sample flight speed... Dimensionally consistent grid coordinates Geometric prior features and local edge features decouple the solver, so as long as a steady-state free surface elevation field PositionZ can be provided, it can be adapted to different CFD sources.
[0080] Step 6: Construct the features to be predicted based on the target speed of the ship at draft T and the grid coordinates of each two-dimensional neutral grid in the free surface region, and input them into the trained waveform prediction model to obtain the free surface waveform prediction results of the ship at draft T and target speed.
[0081] The model inference phase generates the same two-dimensional neutral grid as the model training phase. Then, similar to the training phase, the predicted features are constructed using the grid coordinates of each two-dimensional neutral grid within the target speed and free surface region. These coordinates serve as input to the waveform prediction model, outputting predicted elevations on the two-dimensional neutral grid. The predicted elevations at each two-dimensional neutral grid are then written back into three-dimensional free surface coordinates to obtain the free surface waveform prediction results at draft T and the target speed. Renderable patches can be generated using a mask based on the ship's waterline projection. These patches can be embedded into the CAVE / UE visual pipeline for immersive display or integrated with subsequent hydrodynamic assessments or multidisciplinary data fusion. The prediction results are bound to the two-dimensional neutral grid, ensuring consistency and comparability across speed data.
[0082] The method for constructing the features to be predicted is similar to the method for constructing the sample input features described above. It should be noted that the practice of adding geometric prior features to the features to be predicted to enhance node features is also applicable in the model inference stage, but it needs to be completed in two stages: First, the features to be predicted in the first stage are constructed using the target speed, dimensionally consistent grid coordinates, and local edge features, and input into the trained waveform prediction model to obtain the initial predicted elevation. Then, the geometric prior features of the initial predicted elevation at each two-dimensional neutral grid are calculated on the discrete differential geometry of the two-dimensional neutral grid within the free surface region. These are combined with the target speed, dimensionally consistent grid coordinates, and local edge features to construct the features to be predicted, which are then re-input into the trained waveform prediction model. After one or two message passes for self-consistent refinement, the final predicted elevation is output. By solidifying the "geometric operator" as a non-trainable pre- / bypass module, the operators and templates are shared between training and inference, avoiding the feature mismatch problem of "visible during training but unavailable during inference."
[0083] In one example, after training a waveform prediction model using a sample set of ships at a draft of T=0.5m, the trained waveform prediction model is used to predict the free surface waveform of the ship at a draft of T=0.5m and a target speed of 10m / s (not included in the training). The predicted elevations at each 2D neutral grid can achieve an RMSE of approximately 2%–4% of the labeled elevation dynamic range, an MAE of approximately 1.5%–3%, a Kelvin wedge angle relative error typically less than 5%, and a dominant wavelength relative error less than 4%. On a single A100 or equivalent performance GPU, a steady-state free surface with millions of nodes can be generated in the order of hundreds of milliseconds, achieving an order-of-magnitude speedup compared to the time taken by traditional steady-state CFD, which ranges from minutes to hours, while avoiding the error accumulation and pipeline complexity caused by repeated resampling between grids.
[0084] The above descriptions are merely preferred embodiments of this application, and this application is not limited to the above embodiments. It is understood that other improvements and variations that can be directly derived or conceived by those skilled in the art without departing from the spirit and concept of this application should be considered to be included within the protection scope of this application.
Claims
1. A method for predicting the free surface waveform of a ship based on a neutral grid, characterized in that, The ship free surface waveform prediction method includes: Numerical simulations were conducted on ships under the same draft T and different sample speeds, and a sample set was constructed. Each sample in the sample set is the steady-state free surface elevation field of the ship at the corresponding sample speed. Based on the maximum sample speed during the numerical simulation process Determine the grid step size, and generate a two-dimensional neutral grid independent of the flight speed according to the grid step size. The two-dimensional neutral grid is located within... The plane is parallel to the horizontal plane; Projecting the steady-state free surface elevation field of each sample onto a two-dimensional neutral grid yields the labeled elevations at each two-dimensional neutral grid point within the free surface region. ; The sample input features are constructed based on the sample velocity and the grid coordinates of each two-dimensional neutral grid within the free surface area for each sample. These features are then input into a pre-built waveform prediction model to obtain the predicted elevation at each two-dimensional neutral grid within the free surface area. Based on the marked elevations at each two-dimensional neutral grid point within the free surface area. and predicted elevation Calculate the loss function and train the waveform prediction model; Based on the target speed of the ship at draft T and the grid coordinates of each two-dimensional neutral grid in the free surface region, the features to be predicted are constructed and input into the trained waveform prediction model to obtain the free surface waveform prediction results of the ship at draft T and target speed.
2. The method for predicting ship free surface waveforms according to claim 1, characterized in that, Based on the maximum sample speed in the numerical simulation process Determining the grid step size includes: Based on the maximum sample speed Calculate the shortest target wavelength , It is the acceleration due to gravity; Determine the grid longitudinal step size along the ship's length direction. And determine the lateral step size of the grid along the ship's width direction. Among them, parameters ,parameter .
3. The method for predicting ship free surface waveforms according to claim 1, characterized in that, The generation of a speed-independent two-dimensional neutral grid according to the grid step size includes: A two-dimensional neutral grid, independent of speed, is generated within a preset outward range of the ship according to the grid step size. The preset outward range covers the bow wave initiation disturbance area and provides boundary buffer in the longitudinal forward direction of the ship, accommodates the main wave train, multiple major peak and valley periods and their initial attenuation process in the longitudinal rearward direction of the ship, and covers the main influence area of the Kelvin wedge wave system on both sides of the ship in the transverse direction.
4. The method for predicting the free surface waveform of a ship according to claim 3, characterized in that, The vessel's preset outward extension range covers the longitudinal area along its length, including... The lateral coverage along the width of the ship includes ;in, It is the vertical length of the ship.
5. The method for predicting the free surface waveform of a ship according to claim 1, characterized in that, The waveform prediction model is constructed based on an MGN network. The sample input features are built using the sample velocity and the grid coordinates of each two-dimensional neutral grid within the free surface region for each sample. The grid coordinates of each two-dimensional neutral grid within the free surface region. Dimensional consistency processing is performed to obtain ;in, It is the vertical length of the ship; The elevations at each two-dimensional neutral grid point are calculated using the discrete differential geometry of the two-dimensional neutral grid within the free surface region. Geometric prior features; Determine any two-dimensional neutral grid within the free surface region. and two-dimensional neutral mesh Length of the connecting edge Normalized direction vector and local elevation differences This constitutes a local edge feature; among which, It is a two-dimensional neutral mesh Grid coordinates, It is a two-dimensional neutral mesh Grid coordinates, It is a two-dimensional neutral mesh The marked elevation, It is a two-dimensional neutral mesh Mark the elevation; Combined with sample flight speed Dimensionally consistent grid coordinates The sample input features are obtained from geometric prior features and local edge features.
6. The method for predicting ship free surface waveforms according to claim 1, characterized in that, Projecting the steady-state free surface elevation field of each sample onto a two-dimensional neutral grid yields the labeled elevations at each two-dimensional neutral grid point within the free surface region. include: Projecting the steady-state free surface elevation field of each sample onto a two-dimensional neutral grid yields the labeled elevations at multiple scattered points. The minimum convex polygon is determined based on scattered points as the effective interpolation region. The labeled elevations at each two-dimensional neutral grid within the free surface region of the effective interpolation region are obtained using Delaunay barycentric linear interpolation. The labeled elevations at each two-dimensional neutral grid outside the effective interpolation region are obtained using the radial basis function (RBF). .
7. The method for predicting ship free surface waveforms according to claim 1, characterized in that, The ship free surface waveform prediction method also includes: A mask is generated based on the ship's waterline projection at draft T. The two-dimensional neutral grid outside the mask area is determined to belong to the two-dimensional neutral grid within the free surface area. The elevations of the two-dimensional neutral grid points within the mask area are then labeled. The value is assigned to NaN, or the weights of the two-dimensional neutral grid located within the mask are reset to 0 when training the waveform prediction model.
8. The method for predicting the free surface waveform of a ship according to claim 1, characterized in that, Based on the marked elevations at each two-dimensional neutral grid point within the free surface area and predicted elevation The loss function is calculated as follows: Based on the marked elevations at each two-dimensional neutral grid point within the free surface area and predicted elevation Calculate elevation prediction loss ;in, It is the number of two-dimensional neutral grids within the free surface region. It is a set of two-dimensional neutral grids within the free surface region. Represents any two-dimensional neutral grid within the free surface region. The elevation marking at that location, Represents any two-dimensional neutral grid within the free surface region. Predicted elevation at the location; Based on the marked elevations at each two-dimensional neutral grid point within the free surface area and predicted elevation The uniformity in local slope and curvature yields the gradient curvature uniformity regularization term. ; Based on the marked elevations at each two-dimensional neutral grid point within the free surface area and predicted elevation The uniformity in dominant wavelength and wavenumber energy distribution yields a lightweight spectral uniformity regularization term. ; Calculate the loss function , and These are the coefficients of two regularization terms.
9. The method for predicting the free surface waveform of a ship according to claim 8, characterized in that, Gradient curvature consistency regularization term The calculation formula is: in, Indicates elevation marking In a two-dimensional neutral grid gradient at, Indicates elevation marking In a two-dimensional neutral grid Along The first derivative of the direction, Indicates elevation marking In a two-dimensional neutral grid Along The first derivative in the direction; Indicates predicted elevation In a two-dimensional neutral grid gradient at, Indicates predicted elevation In a two-dimensional neutral grid Along The first derivative of the direction, Indicates predicted elevation In a two-dimensional neutral grid Along The first derivative in the direction; This indicates the calculation of the L2 norm; Represents the coefficient of the regularization term; Indicates elevation marking In a two-dimensional neutral grid The average curvature at that point and , Indicates elevation marking In a two-dimensional neutral grid Along The second derivative of the direction, Indicates elevation marking In a two-dimensional neutral grid Along The second derivative of the direction; Indicates predicted elevation In a two-dimensional neutral grid The average curvature at that point and , Indicates predicted elevation In a two-dimensional neutral grid Along The second derivative of the direction, Indicates predicted elevation In a two-dimensional neutral grid Along The second derivative in the direction.
10. The method for predicting the free surface waveform of a ship according to claim 8, characterized in that, Calculate the lightweight spectral consistency regularization term include: Label the elevation at each two-dimensional neutral grid point within the free surface region. After removing the mean and windowing, a two-dimensional Fourier transform is performed to obtain the normalized spatial wavenumber spectrum energy distribution. ; Predicted elevations at each two-dimensional neutral grid point within the free surface region After removing the mean and windowing, a two-dimensional Fourier transform is performed to obtain the normalized spatial wavenumber spectrum energy distribution. ; Based on the energy distribution of the normalized spatial wavenumber spectrum and normalized spatial wavenumber spectrum energy distribution Calculate the lightweight spectral consistency regularization term using the following formula. : in, For discrete wavenumber bandwidth determined based on the dominant wavelength, It is a two-dimensional space wavenumber pair.