Method and device for rapidly predicting wave-making resistance coefficient based on three-dimensional hull point cloud

Abstract

The application discloses a wave-making resistance coefficient fast prediction method taking a ship body three-dimensional type value point cloud as input, and belongs to the technical field of ship design and hydrodynamic performance prediction. The method takes the ship body three-dimensional point cloud as input, does not need to depend on specific geometric parameterization modeling technology, and avoids the dependence of traditional approximate models on parameterization selection. Specifically, a ship body surface three-dimensional type value point cloud is generated; deterministic farthest point sampling is performed on the point cloud; a graph neural network model of a multi-neighborhood parallel feature extraction architecture is constructed; complementary learning of local geometric details and global line features of the ship body is realized; and the decision logic of the gradient weighted heat map analysis model is verified to be consistent with the wave-making mechanism. The application can accurately predict the wave-making resistance coefficient of the ship body, significantly improve the prediction accuracy and stability, and provide an explainable analysis, thereby providing efficient and reliable technical support for ship type optimization design.

Description

Technical Field

[0001] This application relates to the field of ship design and hydrodynamic performance prediction technology, specifically to a method and device for rapid prediction of wave-making drag coefficient based on the three-dimensional shape value point cloud of the hull as input. Background Technology

[0002] In the early stages of ship design, especially during hull optimization, rapid performance evaluation and selection of numerous design options are necessary. Wave-making resistance is a significant component of a ship's total resistance, and its rapid and accurate prediction is crucial for improving ship energy efficiency and meeting regulatory requirements such as the International Maritime Organization's Energy Efficiency Design Index.

[0003] Currently, ship performance forecasting mainly relies on two methods: computational fluid dynamics simulation and approximate models (also known as surrogate models or meta-models). Computational fluid dynamics simulation methods offer high accuracy and reliable results, but the cost of a single simulation is high and the cycle is long, making it difficult to support the rapid selection of massive number of options in the early design phase. To balance evaluation efficiency and accuracy, approximate model techniques are widely used in ship hull optimization. These methods (such as Kriging, Co-Kriging, and radial basis function models) achieve rapid performance evaluation by constructing a mathematical mapping relationship between ship design parameters (such as main dimensions and hull line control parameters) and target performance (such as drag coefficient). However, existing rapid forecasting methods based on approximate models have the following significant drawbacks:

[0004] Strong dependence on parametric modeling: The establishment and prediction of such models heavily rely on a pre-defined geometric parameterization system. The models can only handle ship shape changes described by these specific parameters, and lack the ability to represent and predict local geometric details not captured by the parameters (such as small bends, curvature abrupt changes, etc.), resulting in limited model generalization.

[0005] Insufficient universality: Different ship type series or design systems may employ completely different parametric methods. Approximate models built based on a specific parametric method are difficult to transfer and apply to other parametric systems or ship types with unknown original parameters, which is not conducive to building a unified and universal rapid prediction database and platform for ship performance.

[0006] Information loss: The parameterization process is essentially a discrete and abstract mathematical description of a continuous hull surface, which inevitably results in the loss of some original geometric information, especially high-frequency local details, which may have a significant impact on wave-making resistance.

[0007] In recent years, with the development of deep learning in the field of computer vision, some studies have attempted to bypass parameterization and directly convert ship geometry into images (input to 2D convolutional neural networks) or voxels (input to 3D convolutional neural networks) for feature learning and performance prediction. While these methods reduce the dependence on manually defined parameters, they introduce new problems: mapping 3D surfaces to 2D images or regular 3D meshes requires complex preprocessing such as geometric unfolding, rendering, or voxelization, which is cumbersome and may introduce distortion or information loss; at the same time, the resolution of the image or voxels and the choice of viewpoint have a significant impact on prediction accuracy.

[0008] Therefore, there is an urgent need for a new method for rapid performance prediction that can directly process raw hull geometry information, requires no complex parameterization or rasterization preprocessing, and can effectively capture local and global geometric features. Summary of the Invention

[0009] The main objective of this application is to provide a rapid prediction method for wave-making drag coefficient based on three-dimensional hull shape point cloud as input, including the following steps:

[0010] Step S1: Obtain the 3D point cloud of multiple ship hulls;

[0011] Step S2: Sample the three-dimensional point cloud of the multiple ship hulls to obtain a target point cloud containing a fixed number of points;

[0012] Step S3: Construct a graph neural network prediction model. The model takes the target point cloud as input and the wave drag coefficient as output. The model includes a parallel multi-neighborhood feature extraction module for extracting the geometric features of the target point cloud from different neighborhood scales.

[0013] Step S4: Train the graph neural network prediction model using a sample dataset containing the three-dimensional shape value point cloud of the multiple ship hulls and the corresponding wave-making drag coefficients;

[0014] Step S5: Input the target point cloud of the hull to be predicted into the trained graph neural network prediction model to obtain the corresponding predicted value of the wave-making drag coefficient.

[0015] In one embodiment, the step of obtaining the three-dimensional shape point cloud of multiple ship hulls includes:

[0016] A baseline ship type is selected as the parent type. A surface deformation method based on radial basis functions is used to generate a set of geometrically continuously changing ship type variant samples by perturbing the control points on the parent type surface.

[0017] For each generated ship shape variant sample, the three-dimensional coordinates of discrete points are collected from the corresponding digital surface model to form a three-dimensional shape point cloud representing the geometric shape of the ship hull;

[0018] By using computational fluid dynamics numerical simulation, the wave-making drag coefficient of the ship variant sample under predetermined navigation conditions is calculated, and the wave-making drag coefficient is used as the hydrodynamic performance label of the corresponding three-dimensional shape value point cloud, thereby constructing a training dataset of geometric point cloud-performance ground truth pairing.

[0019] In one embodiment, the step of sampling the three-dimensional shape point clouds of multiple ship hulls to obtain a target point cloud containing a fixed number of points includes:

[0020] Calculate the geometric centroid of the multiple three-dimensional point clouds of the ship hull;

[0021] The point closest to the geometric centroid is selected as the first sampling point;

[0022] Starting from the first sampling point, recursive sampling is performed according to the maximum and minimum distance principle until the number of sampling points reaches the target point cloud with a preset fixed number of points.

[0023] In one embodiment, the step of constructing a graph neural network prediction model, wherein the model takes the target point cloud as input and the wave-making drag coefficient as output, includes a parallel multi-neighborhood feature extraction module for extracting geometric features of the target point cloud from different neighborhood scales, comprising:

[0024] In the first layer of the graph neural network prediction model, at least two parallel dynamic graph convolutional branches are constructed. Each branch is configured with different k-nearest neighbor parameters to construct a local neighborhood graph. The first branch uses a small k value to focus on extracting local high-frequency geometric details on the hull surface, while the second branch uses a large k value to capture the low-frequency hull line trend features of the entire hull.

[0025] The output features of each parallel dynamic graph convolution branch are concatenated along the channel dimension to form a multi-scale fusion feature matrix. Then, a shared multilayer perceptron is used to reduce the dimensionality and integrate the fusion features to obtain geometric features that include both local and global features.

[0026] The geometric features are input into several subsequent standard graph convolutional layers for deep feature abstraction and refinement, and then aggregated into a fixed-dimensional global hull feature vector through global pooling.

[0027] In one embodiment, the parallel multi-neighborhood feature extraction module is set in the first feature extraction layer of the prediction model and includes at least three EdgeConv branches with different k values, where k represents the number of nearest neighbors selected when constructing the neighborhood graph, and the k values ​​are 10, 20 and 30 respectively.

[0028] In one embodiment, the step of training the graph neural network prediction model using a sample dataset containing three-dimensional shape value point clouds of the plurality of ship hulls and corresponding wave-making drag coefficients includes:

[0029] The sample dataset is divided into a training subset, a validation subset, and a test subset according to a preset ratio; the coordinate data of all three-dimensional point clouds in the training subset are normalized, and the corresponding wave drag coefficient labels are also normalized.

[0030] The graph neural network prediction model is supervised learning using a training subset. Predicted values ​​are calculated using forward propagation, and the mean squared error between the predicted and true values ​​is used as the loss function. The model parameters are iteratively updated using a backpropagation algorithm combined with a stochastic gradient descent optimizer. The model performance is evaluated using the validation subset after each round of training to monitor the training process.

[0031] Training stops when the loss function value of the graph neural network prediction model no longer decreases significantly on the validation subset or reaches the preset training rounds, and the optimal model parameters are saved.

[0032] In one embodiment, the step of inputting the target point cloud of the hull to be predicted into the trained graph neural network prediction model to obtain the corresponding predicted wave-making drag coefficient includes:

[0033] The three-dimensional shape value point cloud data of the hull to be predicted is obtained, and the same deterministic sampling algorithm as in the training phase is used to process it into a target point cloud with a fixed number of points. The point cloud coordinates are then normalized in the same way as the training data.

[0034] The normalized target point cloud data is input into the trained graph neural network prediction model. Multi-scale geometric features are extracted through the model’s built-in parallel multi-neighborhood feature extraction module, and forward propagation calculation is performed through the subsequent feature aggregation and regression network.

[0035] Obtain the normalized predicted wave drag coefficient from the model output, and convert the predicted value into a wave drag coefficient prediction result with actual physical dimensions by applying the opposite inversion operation to the training phase.

[0036] In one embodiment, the method further includes:

[0037] Based on gradient-weighted class activation mapping, a hull surface thermal map corresponding to the predicted wave-making drag coefficient is generated to visualize the key geometric regions of the hull on which the model decision is based.

[0038] A rapid prediction device for wave-making drag coefficient based on three-dimensional hull shape point cloud as input, the device comprising:

[0039] The data acquisition module is used to acquire three-dimensional point clouds of multiple ship hulls;

[0040] The data processing module is used to sample and process the three-dimensional point cloud of the multiple ship hulls to obtain a target point cloud containing a fixed number of points;

[0041] The model building module is used to build a graph neural network prediction model. The model takes the target point cloud as input and the wave drag coefficient as output. The model includes a parallel multi-neighborhood feature extraction module for extracting the geometric features of the target point cloud from different neighborhood scales.

[0042] The model training module is used to train the graph neural network prediction model using a sample dataset containing the three-dimensional shape value point cloud of the multiple ship hulls and the corresponding wave-making drag coefficients.

[0043] The model prediction module is used to input the target point cloud of the hull to be predicted into the trained graph neural network prediction model to obtain the corresponding predicted value of the wave-making drag coefficient.

[0044] Therefore, this application has the following beneficial effects:

[0045] This application provides a method for rapid prediction of wave-making drag coefficient based on three-dimensional shape value point cloud of ship hull as input, including the following steps:

[0046] Step S1: Obtain the 3D point cloud of multiple ship hulls;

[0047] Step S2: Sample the three-dimensional point cloud of the multiple ship hulls to obtain a target point cloud containing a fixed number of points;

[0048] Step S3: Construct a graph neural network prediction model. The model takes the target point cloud as input and the wave drag coefficient as output. The model includes a parallel multi-neighborhood feature extraction module for extracting the geometric features of the target point cloud from different neighborhood scales.

[0049] Step S4: Train the graph neural network prediction model using a sample dataset containing the three-dimensional shape value point cloud of the multiple ship hulls and the corresponding wave-making drag coefficients;

[0050] Step S5: Input the target point cloud of the hull to be predicted into the trained graph neural network prediction model to obtain the corresponding predicted value of the wave-making drag coefficient. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is a system flowchart of a method for rapid prediction of wave-making drag coefficient based on three-dimensional shape value point cloud of ship hull as input;

[0053] Figure 2 This is an example diagram of the S60 mother ship model based on a rapid prediction method for wave-making drag coefficient using the three-dimensional shape value point cloud of the hull as input.

[0054] Figure 3 This is an example S60 discrete point cloud diagram of a rapid prediction method for wave-making drag coefficient based on the three-dimensional shape value point cloud of the ship hull as input.

[0055] Figure 4 This is a sampled point cloud image of a rapid prediction method for wave-making drag coefficient based on the three-dimensional shape value point cloud of the ship hull as input.

[0056] Figure 5 This is a schematic diagram of the PB-GraphPR network structure for a fast prediction method of wave-making drag coefficient based on the three-dimensional shape value point cloud of the ship hull as input;

[0057] Figure 6 This is the overall architecture diagram of a rapid prediction method for wave-making drag coefficient based on the three-dimensional shape value point cloud of the ship hull as input;

[0058] Figure 7 The results are a comparison of the training set of a rapid prediction method for wave-making drag coefficient based on the three-dimensional shape value point cloud of the ship hull as input.

[0059] Figure 8 It is a side-view, port-side, and top-view heat map of a rapid prediction method for wave-making drag coefficient based on the three-dimensional shape value point cloud of the hull as input. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0061] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application.

[0062] To address the shortcomings of existing rapid prediction methods for ship wave-making drag, which heavily rely on specific geometric parameterization models, struggle to capture local details, and lack versatility, this application proposes a rapid prediction method for wave-making drag coefficients based on the input of a three-dimensional point cloud of the ship's hull shape. The core of this method lies in abandoning the traditional intermediate parameterization steps and directly using a discrete set of three-dimensional points on the ship's surface as a unified geometric description. Furthermore, an innovative graph neural network structure is employed to achieve end-to-end performance mapping.

[0063] First, the acquired raw hull shape point cloud undergoes deterministic farthest point sampling to retain key geometric features stably with a fixed number of points (1024). Then, a regression model based on a dynamic graph convolutional neural network is constructed. The core innovation of this model lies in its first-layer feature extraction module, which employs a parallel multi-neighbor architecture. This involves deploying multiple edge convolutional branches with different receptive fields (distinguished by the number of k nearest neighbors). The smaller neighbor branches are specifically designed to capture high-frequency details of the hull's local areas (such as bilge angles and stern plate edges), while the larger neighbor branches are responsible for perceiving the overall hull shape trends, such as longitudinal fullness distribution. Features extracted at different scales are fused and fed into subsequent network layers for deep integration and global information aggregation. Finally, the regression network outputs a predicted wave-making drag coefficient.

[0064] This application, by directly processing point clouds, completely eliminates the reliance on pre-defined parameterization systems, greatly enhancing the model's universality for ship type data from different sources. The innovative parallel multi-neighborhood design enables the model to simultaneously and complementaryly learn local geometric abrupt changes and global morphological features, thereby significantly improving forecast accuracy and stability. Furthermore, this method can be combined with gradient visualization technology to generate heatmaps, intuitively revealing the key hull regions upon which the model's decisions are based. This not only enhances the interpretability and credibility of the results but also provides direct guidance for targeted ship type optimization. The entire process requires no complex mesh generation or image rendering, and preprocessing is simple, achieving truly efficient, universal, and accurate rapid forecasting.

[0065] This application provides a method for rapid prediction of wave-making drag coefficient based on three-dimensional hull shape point cloud as input, including steps S1 to S5, as described above. Figure 1 , Figure 1 This is a system flowchart of a method for rapid prediction of wave-making drag coefficient based on the three-dimensional shape value point cloud of the ship's hull as input.

[0066] Step S1: Obtain the 3D point cloud of multiple ship hulls;

[0067] Step S2: Sample the three-dimensional point cloud of the multiple ship hulls to obtain a target point cloud containing a fixed number of points;

[0068] Step S3: Construct a graph neural network prediction model. The model takes the target point cloud as input and the wave drag coefficient as output. The model includes a parallel multi-neighborhood feature extraction module for extracting the geometric features of the target point cloud from different neighborhood scales.

[0069] Step S4: Train the graph neural network prediction model using a sample dataset containing the three-dimensional shape value point cloud of the multiple ship hulls and the corresponding wave-making drag coefficients;

[0070] Step S5: Input the target point cloud of the hull to be predicted into the trained graph neural network prediction model to obtain the corresponding predicted value of the wave-making drag coefficient.

[0071] Specifically, in this embodiment, this application provides a method for rapid prediction of wave-making drag coefficient based on a three-dimensional point cloud of the ship's hull as input. This method aims to overcome the dependence of existing technologies on specific geometric parameterization, achieving efficient, accurate, and universal performance prediction by directly processing raw point cloud data and utilizing an innovative neural network architecture. (Refer to...) Figure 1 The system flowchart shown below illustrates that the method includes the following specific steps S1 to S5.

[0072] Step S1: Obtain the three-dimensional point cloud of multiple ship hulls.

[0073] This step aims to construct the geometric dataset required for model training and testing. Specifically, the 3D shape point cloud is a set of discrete points describing the shape of the hull's outer surface, with each point represented by its 3D spatial coordinates. Definition. In a preferred embodiment, a baseline ship type is selected as the parent type;

[0074] Using Series 60 (S60) in Table 1 as the parent model, 1900 ship form samples were generated using the radial basis function (RBF) deformation method, and the SHIPFLOW software was used for calculation. Values ​​are used to construct the dataset.

[0075] Table 1 Main parameters of S60 mother mold

[0076]

[0077] This application employs a surface deformation technique based on radial basis functions to generate a large number of ship hull variants with continuously changing geometry within the neighborhood of the parent hull by perturbing the surface control points. Discrete points are uniformly extracted from the digitized surface model of each variant to form original three-dimensional hull value point cloud samples. Simultaneously, for each ship hull variant, its wave-making drag coefficient under specific operating conditions is calculated using high-fidelity computational fluid dynamics (CFD) simulation, serving as the performance label, i.e., the true value, for that point cloud sample. Thus, a sample dataset consisting of "geometric point cloud - performance label" pairs is constructed.

[0078] Step S2: Sample the three-dimensional point cloud of the multiple ship hulls to obtain a target point cloud containing a fixed number of points.

[0079] Original point clouds typically have a large number of points, and the number of points varies between different samples. Directly inputting them into a neural network leads to low computational efficiency and is not conducive to batch processing. The purpose of this step is to downsample each original point cloud, unifying it into a regular representation with a fixed number of points while preserving key geometric features. This application preferably employs a deterministic farthest point sampling (FPS) method based on the centroid nearest point. The specific process is as follows:

[0080] For any given original point cloud, the geometric centroid of all its points is first calculated. Then, the point closest to this centroid is selected as the first sampling point. Starting from this point, an iterative sampling strategy is adopted: in each iteration, the point furthest from the currently selected sampling point set is added to the set. This process continues until the number of sampling points reaches a preset fixed target value M (e.g., M=1024). This method eliminates the uncertainty of sampling results caused by random initialization through deterministic initial point selection, ensuring that the same ship type obtains a completely consistent target point cloud in multiple processing, laying the foundation for the stability of model training. The target point cloud obtained after sampling has a relatively high point density in areas where the hull curvature changes significantly (such as the bow, stern, and bilge), effectively preserving key geometric information affecting hydrodynamic performance.

[0081] The outer surface of the ship's hull is extracted as a three-dimensional point cloud, such as... Figure 2 and Figure 3 As shown. The three-dimensional coordinates of the ship's hull are used. Bow , starboard Vertical Define the point set and the target number of points:

[0082]

[0083] For points, This represents the number of target sampling points.

[0084] Due to the large number of discrete point clouds ( In the process of building a neural network, this leads to high computational complexity and increased computational cost, which is not conducive to achieving rapid forecasting. Therefore, this application improves upon the farthest point sampling algorithm and its initial sampling point selection method, fixing the number of points to 1024 while ensuring that the ship's geometric features remain unchanged. The specific improvements are as follows:

[0085] The FPS algorithm, by randomly selecting initial points, introduces sampling uncertainty into subsequent forecasting processes, affecting forecast stability. To address this, a deterministic farthest-point sampling method based on the nearest centroid is proposed. First, the geometric centroid of the point cloud is selected. The nearest point is used as the first sampling point. , give Calculation and Choice:

[0086]

[0087]

[0088] Select the first sampling point Then, a greedy recursive approach is used based on the maximum-minimum distance principle until the target number of points is reached. This method has the same computational complexity as standard FPS, where... The total number of point clouds, The target number of sampling points. This sampling strategy enables stable sampling in key areas of the ship's geometry—such as the highly curved bow, stern, and bilge surfaces.

[0089] Improve the point cloud after FPS sampling, such as Figure 4 As shown, this sampling method can accurately process the original point cloud, preserving the ship's main outline and key geometry while compressing the number of points, achieving uniform geometric coverage of the ship's global outline. Compared to random initialization, the deterministic farthest point sampling method based on the centroid nearest point ensures that the sampling results are completely consistent across multiple training and inference processes for the same input, providing a reliable geometric foundation for subsequent feature learning based on k-nearest neighbors.

[0090] Step S3: Construct a graph neural network prediction model.

[0091] This step constructs a core prediction model for mapping point cloud geometry to the wave-making drag coefficient. The model takes the target point cloud (M×3 shape) obtained in step S2 as input and outputs a scalar value of the wave-making drag coefficient. This model is based on a dynamic graph convolutional neural network architecture, and its core feature is the inclusion of parallel multi-neighborhood feature extraction modules.

[0092] The parallel multi-neighborhood feature extraction module is typically placed in the first feature learning layer of the network. It consists of multiple parallel dynamic graph convolutional branches, each using a different number of k-nearest neighbors to construct a local neighborhood graph. For example, one embodiment uses three branches with k values ​​set to 10, 20, and 30, respectively. The branch with a smaller k value (e.g., k=10) has a smaller receptive field and acts as a "local detail detector," focusing on capturing high-frequency geometric features on the hull surface, such as bends and abrupt curvature changes. The branch with a larger k value (e.g., k=30) has a larger receptive field and acts as a global context perceptron, focusing on extracting low-frequency trend features such as the hull's longitudinal contour and overall fullness distribution. After each branch independently extracts features from the input point cloud, their outputs are concatenated along the feature channel dimension. Subsequently, a feature fusion layer (e.g., a shared multilayer perceptron MLP) integrates the concatenated multi-scale features into a unified feature representation. Subsequently, the network can continue to connect several standard graph convolutional layers for deeper feature abstraction and refinement. Finally, through a global pooling layer (such as global max pooling), the features of the entire point cloud are aggregated into a global description vector, and then a fully connected regression network maps this vector to the final predicted value of the wave drag coefficient.

[0093] In the Xingbo problem, the local curved surfaces of the hull are just as important as the main elements of the ship. If only a single surface is used for the first layer... =20, in the stage of "closest to the original geometry", scale information on the other side may be lost. Therefore, based on the Dynamic Graph CNN Prediction of Resistance (DGCNN-PR), this application proposes an improved PB-GraphPR (Parallel-Branch Graph-based Prediction of Resistance) graph neural network prediction model to improve the accuracy and stability of the model's predictions. A schematic diagram of the PB-GraphPR network structure of this application is shown below. Figure 5 As shown, the specific content is as follows:

[0094] PB-GraphPR: First-layer parallel EdgeConv ( =10 / 20 / 30 (32 channels each) → Channel splicing →MLP(96→64) fusion ; followed by two layers of EdgeConv( =20) Output , Before reading, the parts are pieced together. Dimensionally upsized via MLP (256→1024) and along Global max pooling; the regression network is the same as DGCNN-PR.

[0095] The core idea is to construct a parallel multi-neighborhood EdgeConv architecture in the first layer. Smaller neighborhood branches act as "geometric high-frequency feature probes," focusing on capturing subtle changes in curvature on the hull surface, such as bilge lines and stern bends. Larger neighborhood branches are responsible for establishing "global context awareness," covering a wider topological region to encode the longitudinal fullness distribution and surface transition trends of the hull. PB-GraphPR integrates local geometric details with overall hull line trends through a feature fusion module, achieving a comprehensive feature representation. This design aims to significantly improve the model's ability to distinguish complex hull features while keeping computational costs manageable, thereby enhancing the accuracy and stability of prediction results.

[0096] Let the neighborhood scale of the parallel branches be... The first-layer parallel connection and fusion process is as follows:

[0097]

[0098]

[0099] Each branch has 32 EdgeConv output channels, which are concatenated to obtain... The features are then fused using MLP (96→64), hence The two floors then adopted a unified design. = 20 single-path EdgeConv integration and upgrade:

[0100]

[0101]

[0102] The output structure of the model is consistent with that of the DGCNN-PR model, first concatenating the channels to obtain the output. Then, after point-by-point dimensionality increase, global max pooling is performed and the result is fed into a regression network with the same structure.

[0103] Step S4: Train the graph neural network prediction model using the sample dataset.

[0104] This step aims to optimize model parameters through a data-driven approach. The dataset constructed in step S1 is divided into training, validation, and test sets. Supervised learning of the model constructed in step S3 is performed using the training set. Before training, the coordinates of the input point cloud and the output labels need to be normalized. The training process aims to minimize the error between the predicted values ​​and the CFD ground truth, typically using mean squared error as the loss function, and iteratively updating the model weights using backpropagation and optimizers such as Adam. The validation set is used to monitor the training process, prevent overfitting, and allow for hyperparameter tuning. Training continues until the model's performance on the validation set stabilizes and converges.

[0105] Step S5: Input the target point cloud of the ship hull to be predicted into the trained model for prediction.

[0106] For a new hull design requiring wave-making drag prediction, its 3D surface model is first acquired and converted into a 3D shape point cloud. Then, using the same deterministic sampling method as in step S2, it is processed into a target point cloud with the same fixed number of points M, and the same coordinate normalization is performed. Finally, this processed point cloud is directly input into the graph neural network prediction model trained in step S4. The model performs forward propagation calculations and outputs the predicted wave-making drag coefficient of the hull under specified operating conditions in almost real-time. This method eliminates the dependence on hull parameterization and achieves rapid end-to-end prediction from raw geometry to performance.

[0107] It is particularly important to note, as shown in the figure, Figure 6 This is a diagram illustrating the overall architecture of a rapid wave-making drag coefficient prediction method based on 3D point clouds of ship hull geometry as input. This application uses 3D point clouds of the ship's surface as input to achieve the prediction of wave-making drag coefficients from hull geometry. Regression mapping ,Right now ,in For prediction The operating conditions are Fr = 0.305 and draft T = 0.163 m.

[0108] Input point cloud After improved deterministic farthest point sampling, N=1024 points are retained as network input. The output is normalized to... interval The predicted values ​​are denormalized to physical dimensionless coefficients during evaluation. This application employs two network implementations. ,include:

[0109] (1) Baseline model DGCNN-PR;

[0110] (2) An improved first-layer parallel model PB-GraphPR based on (1). Both are based on dynamic graph k-nearest neighbor construction and EdgeConv to extract local-context features, and finally output the prediction results through a regression network.

[0111] In one embodiment, the step of obtaining the three-dimensional shape point cloud of multiple ship hulls includes:

[0112] A baseline ship type is selected as the parent type. A surface deformation method based on radial basis functions is used to generate a set of geometrically continuously changing ship type variant samples by perturbing the control points on the parent type surface.

[0113] For each generated ship shape variant sample, the three-dimensional coordinates of discrete points are collected from the corresponding digital surface model to form a three-dimensional shape point cloud representing the geometric shape of the ship hull;

[0114] By using computational fluid dynamics numerical simulation, the wave-making drag coefficient of the ship variant sample under predetermined navigation conditions is calculated, and the wave-making drag coefficient is used as the hydrodynamic performance label of the corresponding three-dimensional shape value point cloud, thereby constructing a training dataset of geometric point cloud-performance ground truth pairing.

[0115] Specifically, in this embodiment, acquiring the three-dimensional point clouds of multiple hull shapes is a crucial step in constructing the dataset. This process begins with selecting a representative baseline hull shape as the geometric master. To ensure the diversity and rationality of the generated samples, a surface deformation method based on radial basis functions is employed: by placing control points on the master surface and applying scientific perturbations, the hull surface morphology can be smoothly and continuously changed, thereby systematically generating a set of hull shape variant samples with geometrically continuous changes within the master design space. This method can cover various shape variations, including local details such as bilge lines, bow ingress angle, and global features such as longitudinal fullness, while maintaining the geometric rationality of the hull.

[0116] For each generated hull variant sample, the three-dimensional spatial coordinates of discrete points are collected from its digital surface model, typically a CAD or curved surface model, according to a set density and rules. This set of coordinate points constitutes a three-dimensional shape point cloud representing the hull's geometry. Its coordinates are typically defined as a right-handed coordinate system with the bow as +X, the starboard side as +Y, and the vertical upward direction as +Z. This step transforms a continuous curved surface into a discrete but complete geometric numerical representation.

[0117] To provide accurate supervisory signals for subsequent supervised learning, the true performance values ​​of each ship type sample need to be labeled. Using high-reliability computational fluid dynamics numerical simulation software, numerical calculations were performed on each ship type variant under predetermined navigation conditions, such as specific Froude numbers (Fr) and drafts (T), to accurately solve for its wave-making drag coefficient. This coefficient, as a key hydrodynamic performance indicator, was established as the hydrodynamic performance label for the corresponding 3D hull point cloud sample. Finally, by mapping the point cloud data of each ship type to its wave-making drag coefficient obtained from CFD simulation, a structured "geometric point cloud-true performance value" paired training dataset was constructed, providing a learning foundation for subsequent deep learning-based prediction models that combines geometric diversity with label accuracy.

[0118] In one embodiment, the step of sampling the three-dimensional shape point clouds of multiple ship hulls to obtain a target point cloud containing a fixed number of points includes:

[0119] Calculate the geometric centroid of the multiple three-dimensional point clouds of the ship hull;

[0120] The point closest to the geometric centroid is selected as the first sampling point;

[0121] Starting from the first sampling point, recursive sampling is performed according to the maximum and minimum distance principle until the number of sampling points reaches the target point cloud with a preset fixed number of points.

[0122] Specifically, in this embodiment, the three-dimensional point clouds of multiple ship hulls are sampled to unify the original high-density point clouds with varying point counts into a regular format with a fixed number of points. This preserves key geometric features while improving the efficiency and stability of subsequent neural network processing. This embodiment employs an improved deterministic farthest point sampling algorithm.

[0123] First, for each original 3D point cloud input, its geometric centroid is calculated. The centroid is obtained by the arithmetic mean of the 3D coordinates of all points in the point cloud, representing the spatial distribution center of the point cloud. Then, instead of randomly selecting a starting point, the algorithm chooses the point with the closest Euclidean distance to the geometric centroid as the first sampling point. This deterministic strategy is crucial; it eliminates the randomness of results caused by random initialization in traditional farthest-point sampling, ensuring that the same input point cloud always yields the exact same sampling sequence during repeated processing, laying a solid foundation for the reproducibility of model training and inference.

[0124] After determining the starting point, the algorithm enters the iterative phase. Starting from the first sampling point, a greedy recursive sampling is performed based on the "maximum-minimum distance principle." Specifically, in each iteration, all unsampled points are traversed, and the shortest distance from each point to all points in the current set of selected sampling points is calculated. Then, the point with the largest shortest distance (i.e., the point "farthest" from existing sampling points) is selected as the next sampling point and added to the sampling set. This process is repeated until the number of sampling points reaches a preset fixed target value (e.g., 1024 points). This strategy enables the sampling points to be distributed as evenly and dispersedly as possible in geographic space, thus effectively covering the hull surface contour while significantly compressing the data volume. A relatively high sampling density is achieved, especially in areas with significant curvature changes and rich geometric information (such as the bow, stern, and bilge). Through the above steps, a target point cloud containing a fixed number of points is finally generated for each original hull shape point cloud, stably reflecting its main geometric features and key details. This preprocessing method not only unifies the data scale and reduces computational complexity, but its determinism also ensures the consistency of model inputs, making it an important preprocessing step in building robust and reliable forecasting models.

[0125] In one embodiment, the step of constructing a graph neural network prediction model, wherein the model takes the target point cloud as input and the wave-making drag coefficient as output, includes a parallel multi-neighborhood feature extraction module for extracting geometric features of the target point cloud from different neighborhood scales, comprising:

[0126] In the first layer of the graph neural network prediction model, at least two parallel dynamic graph convolutional branches are constructed. Each branch is configured with different k-nearest neighbor parameters to construct a local neighborhood graph. The first branch uses a small k value to focus on extracting local high-frequency geometric details on the hull surface, while the second branch uses a large k value to capture the low-frequency hull line trend features of the entire hull.

[0127] The output features of each parallel dynamic graph convolution branch are concatenated along the channel dimension to form a multi-scale fusion feature matrix. Then, a shared multilayer perceptron is used to reduce the dimensionality and integrate the fusion features to obtain geometric features that include both local and global features.

[0128] The geometric features are input into several subsequent standard graph convolutional layers for deep feature abstraction and refinement, and then aggregated into a fixed-dimensional global hull feature vector through global pooling.

[0129] Specifically, in this embodiment, constructing a graph neural network prediction model is the core of achieving accurate mapping from hull geometry to wave-making drag coefficient. This model takes a sampled target point cloud with a fixed number of points as input, and its core innovation lies in introducing a parallel multi-neighborhood feature extraction module in the first layer, aiming to simultaneously capture geometric information at different spatial scales.

[0130] Specifically, in the first-layer feature extraction stage of the model, at least two parallel dynamic graph convolution (EdgeConv) branches are constructed. Each branch operates independently but is configured with different k-nearest neighbor parameters (k values) to construct local neighborhood relationship graphs. For example, the first branch uses a smaller k value (e.g., k=10), with a narrow receptive field, enabling it to focus on local high-frequency geometric details on the hull surface and keenly perceive subtle changes in curvature abrupt changes such as the edge of the stern plate and the bilge bend line. Conversely, the second branch uses a larger k value (e.g., k=30), with a wider receptive field, enabling it to capture the overall low-frequency hull line trends and understand macroscopic morphological features such as the transition surface from the bow to the midbody and the longitudinal fullness distribution. This multi-scale parallel design allows the model to simultaneously acquire complementary information from microscopic details to macroscopic contours in the first layer.

[0131] Subsequently, the output features extracted from these two branches are concatenated along the channel dimension to form a feature matrix that integrates multi-scale information. This matrix undergoes dimensionality reduction and deep integration using a shared multilayer perceptron (MLP). This MLP learns how to most effectively weight and fuse features from different scales, ultimately outputting a unified composite geometric feature representation that simultaneously contains local details and global trends.

[0132] This composite feature is fed into subsequent networks for deeper processing. It undergoes further abstraction and refinement through several standard graph convolutional layers, where the network can learn more complex feature interactions and geometric semantics. Finally, a global pooling operation aggregates the features of all points in the point cloud into a fixed-dimensional global hull feature vector. This vector condenses the key geometric information that determines wave-making drag, providing a highly condensed input for the final fully connected regression network to output accurate predictions of the wave-making drag coefficient.

[0133] In one embodiment, the parallel multi-neighborhood feature extraction module is set in the first feature extraction layer of the prediction model and includes at least three EdgeConv branches with different k values, where k represents the number of nearest neighbors selected when constructing the neighborhood graph, and the k values ​​are 10, 20 and 30 respectively.

[0134] Specifically, in this embodiment, the parallel multi-neighborhood feature extraction module, as the core of the model's geometric feature perception, is specifically positioned in the first feature extraction layer of the entire graph neural network prediction model. This strategic location ensures that the model can parse geometric information in parallel at multiple scales when initially processing the raw point cloud coordinates, laying a multi-layered understanding foundation for subsequent deep feature learning.

[0135] The specific architecture of this module includes at least three parallel dynamic graph convolution (EdgeConv) branches. Each branch is structurally similar, but they are distinguished by a key hyperparameter k value, which is the number of nearest neighbors selected when constructing the local neighborhood graph, thus giving them different receptive fields and feature extraction tendencies. In this embodiment, the k values ​​of the three branches are set to 10, 20, and 30, respectively, forming a sequence of receptive fields from smallest to largest.

[0136] The k=10 branch (small neighborhood branch) has the narrowest receptive field. It acts like a high-precision local scanner, focusing on each point in the point cloud and its few closest neighbors. This setup makes it exceptionally sensitive to high-frequency geometric details on the hull surface, accurately capturing minute shape changes in local areas such as abrupt changes in bilge curvature, stern bends, and bow inlet flanges. These details can subtly influence flow separation and vortex generation.

[0137] The k=30 branch (large neighborhood branch) possesses the widest receptive field. Like a wide-angle lens, it covers a larger area around each point in the point cloud. This makes it adept at integrating information and perceiving the low-frequency overall hull line trends and macroscopic contours, such as bow fullness distribution, parallel midbody length, and longitudinal curvature variations—global features closely related to the main mechanisms of wave-making drag.

[0138] The k=20 branch is intermediate, providing a medium-scale perspective. While capturing local features within a certain range, it can also perceive contextual information over a slightly larger area, acting as a bridge between high-frequency details and low-frequency trends, making the transition of multi-scale features smoother and more coherent.

[0139] In one embodiment, the step of training the graph neural network prediction model using a sample dataset containing three-dimensional shape value point clouds of the plurality of ship hulls and corresponding wave-making drag coefficients includes:

[0140] The sample dataset is divided into a training subset, a validation subset, and a test subset according to a preset ratio; the coordinate data of all three-dimensional point clouds in the training subset are normalized, and the corresponding wave drag coefficient labels are also normalized.

[0141] The graph neural network prediction model is supervised learning using a training subset. Predicted values ​​are calculated using forward propagation, and the mean squared error between the predicted and true values ​​is used as the loss function. The model parameters are iteratively updated using a backpropagation algorithm combined with a stochastic gradient descent optimizer. The model performance is evaluated using the validation subset after each round of training to monitor the training process.

[0142] Training stops when the loss function value of the graph neural network prediction model no longer decreases significantly on the validation subset or reaches the preset training rounds, and the optimal model parameters are saved.

[0143] Specifically, in this embodiment, training the graph neural network prediction model is a systematic, data-driven parameter optimization process aimed at enabling the model to learn an accurate mapping from hull point cloud geometry to wave-making drag coefficients. This process includes the following key steps:

[0144] First, data preparation and partitioning are performed. The complete "point cloud-drag coefficient" sample dataset is divided into training, validation, and test subsets according to a preset ratio, such as 1500:200:200. To ensure stable training and accelerate convergence, the 3D coordinates of all point clouds in the training subset are normalized (e.g., by subtracting the mean or dividing by the standard deviation), and the corresponding wave drag coefficient labels are standardized or normalized (e.g., scaled to the [0,1] interval). The validation and test sets use the same preprocessing parameters to ensure consistency in data distribution.

[0145] Following this, the core iterative training phase begins. Supervised learning of the model is performed using a training subset. In each epoch of training, normalized point cloud data is input into the model in mini-batches, and the predicted wave drag coefficient is calculated through forward propagation. The mean squared error between the predicted value and the normalized true value is calculated as the loss function to quantify the current model's prediction error. Next, the gradient of the loss function with respect to all model parameters is calculated using the backpropagation algorithm, and these gradients are used in conjunction with a stochastic gradient descent optimizer to iteratively update the model weights to minimize the loss. After each training epoch, the model performance is evaluated using a validation subset, and the validation loss is calculated. This effectively monitors the training process and promptly identifies signs of overfitting or underfitting.

[0146] Finally, training is terminated and the model is saved. Training continues until the model's loss function value on the validation subset no longer decreases significantly over multiple epochs, or the number of training epochs reaches a preset upper limit. Throughout the training process, a snapshot of the optimal model parameters on the validation set is saved. After training, the finally saved optimal model is evaluated using a completely independent test subset.

[0147] In one embodiment, the step of inputting the target point cloud of the hull to be predicted into the trained graph neural network prediction model to obtain the corresponding predicted wave-making drag coefficient includes:

[0148] The three-dimensional shape value point cloud data of the hull to be predicted is obtained, and the same deterministic sampling algorithm as in the training phase is used to process it into a target point cloud with a fixed number of points. The point cloud coordinates are then normalized in the same way as the training data.

[0149] The normalized target point cloud data is input into the trained graph neural network prediction model. Multi-scale geometric features are extracted through the model’s built-in parallel multi-neighborhood feature extraction module, and forward propagation calculation is performed through the subsequent feature aggregation and regression network.

[0150] Obtain the normalized predicted wave drag coefficient from the model output, and convert the predicted value into a wave drag coefficient prediction result with actual physical dimensions by applying the opposite inversion operation to the training phase.

[0151] Specifically, in this embodiment, the step of inputting the target point cloud of the hull to be predicted into the trained graph neural network prediction model and obtaining the predicted wave-making drag coefficient constitutes the application process of this rapid prediction method in actual engineering. This process ensures end-to-end automated processing from the original hull geometry to the final performance index output, and strictly maintains the data processing specifications consistent with the model training stage to ensure the reliability and accuracy of the prediction.

[0152] This step begins with the acquisition and preprocessing of the data for the hull to be predicted. First, the three-dimensional surface geometry of the hull needs to be acquired, which can be in the form of a CAD model, a surface model, or a direct 3D scanned point cloud. After acquiring the 3D point cloud data, it must be processed using the same deterministic sampling algorithm as in the model training phase (i.e., sampling from the farthest point based on the nearest centroid), resampling it into a target point cloud with the same fixed number of points (e.g., 1024 points). Next, the coordinates of this target point cloud are normalized in the same way as the training data, that is, the coordinates are standardized using the mean and standard deviation calculated and stored in the training set. This step is crucial; it eliminates the influence of dimensions and absolute scale, ensuring that the distribution of the input data matches the distribution seen during model training, which is a prerequisite for the model to reason correctly.

[0153] After preprocessing, the model inference and computation stage begins. The normalized target point cloud data is input into a pre-trained graph neural network prediction model with fixed parameters. The model initiates forward propagation: the data first passes through its core parallel multi-neighborhood feature extraction module, which extracts multi-scale geometric features such as local details and global contours of the point cloud in parallel from different receptive fields (k=10,20,30). After these features are fused, they continue to be passed and calculated layer by layer through subsequent feature aggregation layers in the model, such as convolutional layers, global pooling layers, and fully connected layers of the regression network. Finally, a normalized predicted value of the wave-making drag coefficient is generated at the output layer, for example, a scalar in the interval [0,1].

[0154] Finally, the prediction results are post-processed and output. The directly obtained model output is a normalized value, which needs to be restored to its physical meaning by applying the inverse normalization operation of the training phase. Specifically, the transformation parameters (such as minimum-maximum or mean-standard deviation) recorded during the normalization of the drag coefficient labels during training are used to inversely calculate the scalar value of the model output. Through this step, the predicted value is converted into a wave-making drag coefficient prediction result with actual physical dimensions. This result can then be used as a rapid assessment of the hull's wave-making drag performance under specified operating conditions, for scheme comparison, optimization guidance, or preliminary design decisions.

[0155] To further verify that the PB-GraphPR prediction model proposed in this application has a smaller prediction error, this application conducts error testing on the test set, and the comparison results are as follows: Figure 7 As shown in the figure. The horizontal axis is... The truth value, with the ordinate as Predicted values, axis units are the same. The red dashed line is The ideal fitted line, with blue dots representing the predicted result point set.

[0156] As shown in the figure, the point set of the DGCNN-PR prediction results is basically in The distribution on both sides of the ideal line results in a mean absolute error (MAE) of 2.600 × 10⁻⁵ for the predicted point set, which is a good fit to the true value. The results show that DGCNN-PR can effectively predict ship wave-making drag performance based on point clouds, but the bandwidth of the predicted point set (blue points) is relatively large, and the mean relative error (MRE) is 1.266%, indicating room for improvement in fitting accuracy. Compared with DGCNN-PR, PB-GraphPR's predicted point set is more densely distributed near the ideal line, with an MAE of 1.000×10⁻⁵, significantly reduced overall dispersion, and an MRE of 0.494%, exhibiting a tight diagonal distribution with fewer outliers. PB-GraphPR significantly improves the prediction bias for ship wave-making drag performance. The comparison of evaluation metrics for each model on the test set is shown in Table 2.

[0157] Table 2 Test Set Evaluation Metrics

[0158]

[0159] Compared to DGCNN-PR, the MAE of the PB-GraphPR prediction model is higher. Down to (A decrease of approximately 61.5%), MRE decreased from 1.266% to 0.494% (a decrease of approximately 61.0%). Increased to 0.989.

[0160] The results show that PB-GraphPR significantly reduces absolute and relative errors and improves variance interpretation while maintaining the same sampling and evaluation settings. These results indicate that PB-GraphPR has higher forecast accuracy.

[0161] In one embodiment, the method further includes:

[0162] Based on gradient-weighted class activation mapping, a hull surface thermal map corresponding to the predicted wave-making drag coefficient is generated to visualize the key geometric regions of the hull on which the model decision is based.

[0163] Specifically, in this embodiment, the method further includes a key step to enhance model transparency and interpretability: generating a hull surface thermal map corresponding to the predicted wave-making drag coefficient based on a gradient-weighted class activation mapping method. This step aims to visualize the hull geometry that the model focuses on when making decisions, thereby transforming the model's "black box" predictions into intuitive physical insights.

[0164] In practice, after the model predicts the wave-making drag coefficient of a specific hull point cloud, backpropagation is used to calculate the gradient of the final predicted value with respect to the intermediate feature layers of the model (e.g., the output of the first-layer parallel multi-neighborhood feature extraction module or the fused feature layer). By analyzing these gradients and combining them with the activation values ​​of the corresponding feature layers, the relative contribution or importance weight of each sampling point in the point cloud to the final prediction result can be calculated. These weight values ​​are mapped back to the three-dimensional spatial position of the original hull surface and visualized using color gradients (e.g., using a gradient from blue to red, where red represents high contribution / high sensitivity areas and blue represents low contribution / low sensitivity areas), thus generating a heatmap overlaid on the hull surface. The generated heatmap can intuitively reveal the core geometric regions focused by the model's internal attention mechanism. For example, if the heatmap shows significant highlights (red) in the bow inlet, bulbous bow shape, or bilge transition area, it indicates that the model judges that the geometric features of these regions have a key impact on the currently predicted wave-making drag coefficient.

[0165] Based on gradient-weighted heatmaps, hull features are identified, and the model's sensitive areas and contributions to hull geometry are analyzed for interpretability. From the perspective of ship hydrodynamics and geometric modeling, the geometric features affecting wave-making resistance can be broadly classified into the following two categories:

[0166] 1) Local high-frequency geometric features: refers to areas where the curvature or normal vector changes significantly and drastically, such as the edge of the stern plate, the angle line of the bow inlet, and the bilge profile.

[0167] 2) Global low-frequency geometric characteristics: These refer to the overall morphological trends of the hull over a large spatial range, such as the transition surface from the bow to the midbody and the distribution trend of longitudinal fullness. These characteristics are strongly correlated with parameters such as the block coefficient and the longitudinal position of the center of buoyancy, and determine the overall wave-making interference pattern.

[0168] The first-layer parallel structure of PB-GraphPR contains different neighborhood scales. Branches and fusion nodes. Among them, small neighborhood branches ( Large neighborhood branch ( The fusion node is a three-branch splicing. Later The position of the output of convolution (MLP(96→64)).

[0169] remember For branches In the The point cloud feature map output by the layer, where Indicates the first Each point at the The activation value of each channel.

[0170] To quantify the importance of each feature channel to the final prediction result, this paper utilizes the output of the regression network. Then, backpropagation is performed on the feature map. Define the first... Global importance weights of each feature channel For output Global average of the characteristic gradients of all points in this channel:

[0171]

[0172] Based on this, by weighting and summing the feature maps and applying the ReLU activation function, a heatmap of the sensitivity of several sets is obtained. :

[0173]

[0174] The ReLU function is used to filter feature responses that have a negative impact on the prediction result or are irrelevant. Ultimately, it will... Linear normalization to This yields a point-level heatmap, used to display the impact of each sampling point on the prediction. The relative strength of their contributions. Geometric sensitivity is represented by color spectrum: red (value close to 1) represents a high-sensitivity region, meaning that small geometric changes in this region will significantly affect... Forecast; Blue (value close to 0) represents non-sensitive areas.

[0175] The typical heatmap response of the PB-GraphPR prediction model proposed in this application on the test set is as follows: Figure 8 As shown. By comparing small neighborhoods ( ), Greater Neighborhood ( By examining the characteristic responses of the fusion nodes, we can observe the decoupling and reconstruction process of the model for the two types of features mentioned above.

[0176] Small neighborhood branch: Observe the heatmap on the left ( As can be seen, the high-response heat zone (red area) is highly concentrated at the edge of the stern plate and the bilge lines. From a geometric perspective, the stern is usually the area with the most dramatic curvature abrupt change and the most complex topological structure in the entire ship. This indicates that under a small receptive field, the model is mainly affected by geometry, preferentially capturing these local high-frequency geometric features with significant changes in surface normals.

[0177] Large neighborhood branch: Middle column heatmap ( The data shows that the highlighted area shifts from the stern to cover a large area of ​​the transition surface from the bow to the midhull, reflecting the change in the longitudinal fullness of the hull. This indicates that as the receptive field expands, the model begins to focus on global low-frequency geometric features, that is, capturing the hull line trends that are strongly correlated with the wave-making interferometry pattern.

[0178] Fusion Characteristics: The highlighted hotspots in the rightmost heatmap converge further after fusion, ultimately locking the key features near the bow inlet and bilge guide lines. This demonstrates the model's correction mechanism from "geometrically significant" to "physically significant": although small neighborhood branches have a strong response at the stern, the stern region is significantly suppressed and turns cool in tone in the fused heatmap. According to hydrodynamic principles, wave-making resistance is mainly dominated by the formation and interference of the bow wave system, while the stern is more affected by viscous pressure drag. The model actively discards the geometrically most significant stern features, proving that it has successfully learned the core physical factors of wave-making resistance. This distribution indicates that the model does not simply superimpose geometric features, but adaptively selects the key regions that truly determine wave-making performance based on their physical contribution.

[0179] The vast majority of samples in the test set exhibited the aforementioned consistent thermal distribution, validating the effectiveness of the PB-GraphPR model design: small neighborhood branches are responsible for capturing geometric abrupt changes such as the stern and bilge, while large neighborhood branches are responsible for perceiving the global trend of forebody fullness. More importantly, the fused feature distribution indicates that the model successfully achieved attention calibration from "geometric feature-driven" to "wave-making mechanism-oriented," automatically suppressing stern geometric features that contribute less to wave-making resistance and concentrating the focus on the bow wave source. This result demonstrates that the model does not mechanically memorize shapes but rather learns key physical laws, providing a more intuitive basis for subsequent local fine-tuning of the hull shape to address wave-making performance.

[0180] A rapid prediction device for wave-making drag coefficient based on three-dimensional hull shape point cloud as input, the device comprising:

[0181] The data acquisition module is used to acquire three-dimensional point clouds of multiple ship hulls;

[0182] The data processing module is used to sample and process the three-dimensional point cloud of the multiple ship hulls to obtain a target point cloud containing a fixed number of points;

[0183] The model building module is used to build a graph neural network prediction model. The model takes the target point cloud as input and the wave drag coefficient as output. The model includes a parallel multi-neighborhood feature extraction module for extracting the geometric features of the target point cloud from different neighborhood scales.

[0184] The model training module is used to train the graph neural network prediction model using a sample dataset containing the three-dimensional shape value point cloud of the multiple ship hulls and the corresponding wave-making drag coefficients.

[0185] The model prediction module is used to input the target point cloud of the hull to be predicted into the trained graph neural network prediction model to obtain the corresponding predicted value of the wave-making drag coefficient.

[0186] Specifically, this embodiment also provides a rapid wave-making drag coefficient prediction device based on the three-dimensional shape value point cloud of the ship's hull as input, corresponding to the aforementioned method. This device, through modular design, systematically realizes the entire process from data preparation, model building, training optimization to final prediction. The specific structure of the device is as follows:

[0187] The data acquisition module is responsible for constructing or receiving geometric datasets. Its core function is to acquire three-dimensional point clouds of multiple hulls. This includes generating hull variant samples through parametric deformation methods, extracting their surface discrete point cloud coordinates, and associating them with the corresponding true values ​​of wave-making drag coefficients obtained through CFD simulation calculations, thereby forming complete training sample pairs.

[0188] The data processing module performs normalization preprocessing on the received or generated point clouds. Its main task is to sample the 3D shape point clouds of multiple ship hulls. Specifically, it adopts a deterministic farthest point sampling algorithm based on the nearest centroid to uniformly sample the original point clouds of different densities into a target point cloud containing a fixed number of points (such as 1024 points), and normalizes the coordinates to provide the model with a regular input that is scale-uniform and preserves features.

[0189] The model building module is the core technology of the device, used to construct a graph neural network prediction model. The model implemented by this module takes the processed target point cloud as input and the wave-making drag coefficient scalar as output. Its architectural innovation lies in the integration of a parallel multi-neighborhood feature extraction module. This module achieves synchronous and complementary feature extraction of local high-frequency details and global low-frequency hull line trends by setting multiple dynamic graph convolution branches with different k values ​​in parallel at the first layer of the network, laying a structural foundation for high-precision forecasting.

[0190] The model training module optimizes the constructed model using the prepared sample dataset. This module trains the graph neural network prediction model using the sample dataset, performing standard deep learning training procedures including dataset partitioning, loss calculation (such as mean squared error), backpropagation, and parameter iterative updates. It also uses a validation set to monitor the training status to prevent overfitting, and finally outputs a fully trained model with optimal parameters.

[0191] The model prediction module is the final application interface of the device, used to perform rapid forecasting tasks. After the user or system inputs the geometric information of the hull to be predicted, this module calls the data processing flow to generate the target point cloud, and inputs it into the trained graph neural network prediction model. Through one forward propagation calculation, the corresponding wave-making drag coefficient prediction value is quickly obtained, achieving end-to-end second-level performance evaluation.

[0192] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0193] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0194] It should be particularly noted that, through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, or of course, by hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0195] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for rapid prediction of wave-making drag coefficient based on three-dimensional hull shape point cloud as input, characterized in that, Includes the following steps: Step S1: Obtain the 3D point cloud of multiple ship hulls; Step S2: Sample the three-dimensional point cloud of the multiple ship hulls to obtain a target point cloud containing a fixed number of points; Step S3: Construct a graph neural network prediction model. The model takes the target point cloud as input and the wave drag coefficient as output. The model includes a parallel multi-neighborhood feature extraction module for extracting the geometric features of the target point cloud from different neighborhood scales. Step S4: Train the graph neural network prediction model using a sample dataset containing the three-dimensional shape value point cloud of the multiple ship hulls and the corresponding wave-making drag coefficients; Step S5: Input the target point cloud of the hull to be predicted into the trained graph neural network prediction model to obtain the corresponding predicted value of the wave-making drag coefficient.

2. The method according to claim 1, characterized in that, Step S1, the step of obtaining the three-dimensional point cloud of multiple ship hulls, includes: A baseline ship type is selected as the parent type. A surface deformation method based on radial basis functions is used to generate a set of geometrically continuously changing ship type variant samples by perturbing the control points on the parent type surface. For each generated ship shape variant sample, the three-dimensional coordinates of discrete points are collected from the corresponding digital surface model to form a three-dimensional shape point cloud representing the geometric shape of the ship hull; By using computational fluid dynamics numerical simulation, the wave-making drag coefficient of the ship variant sample under predetermined navigation conditions is calculated, and the wave-making drag coefficient is used as the hydrodynamic performance label of the corresponding three-dimensional shape value point cloud, thereby constructing a training dataset of geometric point cloud-performance ground truth pairing.

3. The method according to claim 1, characterized in that, Step S2, the step of sampling the three-dimensional point clouds of multiple ship hulls to obtain a target point cloud containing a fixed number of points, includes: Calculate the geometric centroid of the multiple three-dimensional point clouds of the ship hull; The point closest to the geometric centroid is selected as the first sampling point; Starting from the first sampling point, recursive sampling is performed according to the maximum and minimum distance principle until the number of sampling points reaches the target point cloud with a preset fixed number of points.

4. The method according to claim 1, characterized in that, In step S3, the construction of the graph neural network prediction model, wherein the model takes the target point cloud as input and the wave drag coefficient as output, and the model includes a parallel multi-neighborhood feature extraction module for extracting geometric features of the target point cloud from different neighborhood scales, includes: In the first layer of the graph neural network prediction model, at least two parallel dynamic graph convolutional branches are constructed. Each branch is configured with different k-nearest neighbor parameters to construct a local neighborhood graph. The first branch uses a small k value to focus on extracting local high-frequency geometric details on the hull surface, while the second branch uses a large k value to capture the low-frequency hull line trend features of the entire hull. The output features of each parallel dynamic graph convolution branch are concatenated along the channel dimension to form a multi-scale fusion feature matrix. Then, a shared multilayer perceptron is used to reduce the dimensionality and integrate the fusion features to obtain geometric features that include both local and global features. The geometric features are input into several subsequent standard graph convolutional layers for deep feature abstraction and refinement, and then aggregated into a fixed-dimensional global hull feature vector through global pooling.

5. The method according to claim 4, characterized in that, The parallel multi-neighbor feature extraction module is set in the first feature extraction layer of the prediction model and includes at least three EdgeConv branches with different k values, where k represents the number of nearest neighbors selected when constructing the neighborhood graph, and the k values ​​are 10, 20 and 30 respectively.

6. The method according to claim 1, characterized in that, Step S4, the step of training the graph neural network prediction model using a sample dataset containing the three-dimensional shape value point cloud of the multiple ship hulls and the corresponding wave-making drag coefficients, includes: The sample dataset is divided into a training subset, a validation subset, and a test subset according to a preset ratio; the coordinate data of all three-dimensional point clouds in the training subset are normalized, and the corresponding wave drag coefficient labels are also normalized. The graph neural network prediction model is supervised learning using a training subset. Predicted values ​​are calculated using forward propagation, and the mean squared error between the predicted and true values ​​is used as the loss function. The model parameters are iteratively updated using a backpropagation algorithm combined with a stochastic gradient descent optimizer. The model performance is evaluated using the validation subset after each round of training to monitor the training process. Training stops when the loss function value of the graph neural network prediction model no longer decreases significantly on the validation subset or reaches the preset training rounds, and the optimal model parameters are saved.

7. The method according to claim 1, characterized in that, Step S5, the step of inputting the target point cloud of the hull to be predicted into the trained graph neural network prediction model to obtain the corresponding predicted wave-making drag coefficient, includes: The three-dimensional shape value point cloud data of the hull to be predicted is obtained, and the same deterministic sampling algorithm as in the training phase is used to process it into a target point cloud with a fixed number of points. The point cloud coordinates are then normalized in the same way as the training data. The normalized target point cloud data is input into the trained graph neural network prediction model. Multi-scale geometric features are extracted through the model’s built-in parallel multi-neighborhood feature extraction module, and forward propagation calculation is performed through the subsequent feature aggregation and regression network. Obtain the normalized predicted wave drag coefficient from the model output, and convert the predicted value into a wave drag coefficient prediction result with actual physical dimensions by applying the opposite inversion operation to the training phase.

8. The method according to claim 1, characterized in that, The method further includes: Based on gradient-weighted class activation mapping, a hull surface thermal map corresponding to the predicted wave-making drag coefficient is generated to visualize the key geometric regions of the hull on which the model decision is based.

9. A rapid prediction device for wave-making drag coefficient based on three-dimensional hull shape point cloud as input, characterized in that, The device includes: The data acquisition module is used to acquire three-dimensional point clouds of multiple ship hulls; The data processing module is used to sample and process the three-dimensional point cloud of the multiple ship hulls to obtain a target point cloud containing a fixed number of points; The model building module is used to build a graph neural network prediction model. The model takes the target point cloud as input and the wave drag coefficient as output. The model includes a parallel multi-neighborhood feature extraction module for extracting the geometric features of the target point cloud from different neighborhood scales. The model training module is used to train the graph neural network prediction model using a sample dataset containing the three-dimensional shape value point cloud of the multiple ship hulls and the corresponding wave-making drag coefficients. The model prediction module is used to input the target point cloud of the hull to be predicted into the trained graph neural network prediction model to obtain the corresponding predicted value of the wave-making drag coefficient.

Images