Ship propeller design optimization method and system based on machine learning

Abstract

The invention provides a ship propeller design optimization method and system based on machine learning, and relates to the technical field of ship propeller design, and the method comprises the steps: building a parameterized curved surface based on a geometric control point coordinate set, converting the parameterized curved surface into a signed distance field (SDF), extracting an SDF zero contour surface to generate an initial grid, and carrying out the gradient optimization of control points to meet the demolding angle constraint, calculating the local thickness of the blade based on the SDF, and predicting shrinkage cavity defect probability distribution by adopting a differentiable thermodynamic model and a spatial-temporal characteristic network; fusing the defect probability and the hydrodynamic performance to construct a target function, reversely propagating the gradient to a geometric control point through a thermal field, a grid and an SDF through differentiable simulation, and driving the gradient to synchronously update; and iteratively executing the process, terminating after the defect probability threshold, the performance tolerance and the convergence condition are met, and outputting the propeller geometric model with excellent hydrodynamic performance and high manufacturability.

Description

Technical Field

[0001] This invention relates to the field of ship propeller design optimization technology, specifically a ship propeller design optimization method and system based on machine learning. Background Technology

[0002] As a core component of a ship's propulsion system, the geometric design of a ship's propeller directly affects propulsion efficiency, cavitation noise, and structural reliability. Modern high-precision propellers typically employ complex three-dimensional twisted blade designs to enhance hydrodynamic performance. However, such geometries face significant challenges during sand casting: thin-walled areas of the blades are prone to shrinkage defects due to excessively rapid solidification rates, while thicker areas, such as the hub connection, suffer from thermal shrinkage due to uneven heat dissipation. Traditional design processes rely on engineers' experience to repeatedly adjust the blade thickness distribution in CAD software, then verify manufacturability through casting simulation, and finally confirm performance indicators through water tunnel testing. This process consumes substantial computational resources and trial production costs, especially for ultra-large propellers used in liquefied natural gas (LNG) ships, where a single design iteration cycle can last for several months.

[0003] In existing technologies, common solutions include using parametric surfaces combined with CFD / CAE tools for multidisciplinary analysis and optimization, or applying optimization strategies based on experimental design and surrogate models to reduce computational costs. Some studies have also attempted to introduce machine learning methods, such as accelerating flow field prediction or building defect classification models through neural networks to assist in performance and manufacturability evaluation. However, these methods still have significant limitations: First, the lack of complete differential coherence between geometric representation and simulation modules leads to the inefficient and inaccurate backpropagation of gradients from design variables to the objective function, and the optimization process relies on discrete iteration and repeated evaluation, resulting in low efficiency. Second, existing machine learning-assisted methods focus more on performance prediction rather than global coupled optimization, failing to incorporate manufacturing defect prediction and hydrodynamic performance into a unified framework for synchronous optimization, thus making it difficult to avoid manufacturability risks in the early design stage.

[0004] Of particular note is that existing methods generally lack an endogenous mechanism for the coordinated optimization of geometry, performance, and process. Specifically, in traditional processes, there is a gradient break between geometric modeling and CFD and defect prediction models. Optimization algorithms cannot simultaneously respond to the sensitivity of performance targets and defect constraints by leveraging gradient information, resulting in slow optimization processes and a tendency to get trapped in local optima. In addition, process constraints such as demolding angle and thickness distribution are often used as a posteriori verification conditions rather than embedded in the optimization target, which means that the design results may still fail to meet casting requirements even after performance targets are met.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a machine learning-based method and system for optimizing ship propeller design, in order to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A machine learning-based method for optimizing ship propeller design, comprising the following steps: Step 1: Construct a parametric surface based on the coordinate set of the geometric control points of the ship propeller blades, and convert it into an initial triangular mesh surface. Calculate the angle between the normal vector of each vertex of the mesh and the casting direction, identify vertices with angles less than the preset demolding angle threshold, and adjust the coordinates of the geometric control points through a gradient optimization algorithm to drive the surface deformation until all vertices meet the demolding angle constraint, and finally generate a triangular mesh surface. Step 2: Calculate the local cross-sectional thickness of the blade based on SDF, input the triangular mesh surface into the differential thermodynamic model to simulate the evolution of the thermal state field during the casting process, and input the thermal state field and the local cross-sectional thickness into the spatiotemporal feature extraction network to output the spatial distribution of the probability of shrinkage defects in the propeller body. Step 3: Combining the spatial distribution of the shrinkage cavity defect probability with hydrodynamic performance, construct an optimization objective function. Through differential simulation link, propagate the gradient of the optimization objective function from the thermal state field through the triangular mesh surface and SDF back to the coordinates of each geometric control point. Based on the gradient information, use the optimization algorithm to synchronously update the coordinates of all geometric control points. Step 4: Repeat steps 1 to 3, iteratively updating the geometric control point coordinate set until the probability of shrinkage defects in the entire domain does not exceed the preset safety threshold, the hydrodynamic performance loss is within the tolerance range, and the optimization objective function converges to a stable range. Terminate the loop and output the propeller geometric model constructed based on the final geometric control point coordinate set.

[0008] Furthermore, the logic for constructing a parametric surface based on the coordinate set of the geometric control points of the ship's propeller blades is as follows: An explicit parameterized surface for the propeller blade is constructed based on the geometric control point coordinate set Q, and the corresponding signed distance field is established. ,in The zero isosurface is the implicit geometric expression of this parameterized surface; The above is obtained by isosurface extraction algorithm The zero isosurface is converted into an initial triangular mesh surface. The normal vector at each vertex of the initial triangular mesh surface is calculated. The normal vector is determined by the gradient direction of the SDF at the vertex. The casting direction refers to the relative motion direction when the mold is opened and the casting is taken out after the molten metal is injected into the mold and solidified into the propeller blade. Point-by-point comparison of the angle between the normal vector of each vertex on the initial triangular mesh surface and the casting direction. Identify all that meet the requirements The vertex, of which The minimum demolding angle threshold is set separately for different regions of the propeller blade: the minimum demolding angle for the pressure surface region of the propeller blade is... The minimum demolding angle of the blade suction surface area is The minimum draft angle for the hub connection area is... And satisfy the constraints. ; For the region where the included angle does not reach the demolding angle threshold: the signed distance field of the parameterized surface with the geometric control point coordinate set Q as the independent variable. This involves calculating the demolding angle violation degree for each vertex and transferring this violation degree's sensitivity with respect to the mesh vertices back to Q along the mapping to obtain the manufacturing constraint gradient. This gradient is then transferred to the geometric control point coordinates via the signed distance field. Based on the manufacturing constraint gradient, Q is updated using constrained numerical optimization to drive local deformation of the parameterized surface. This constrained numerical optimization ensures the reasonableness of the deformation in the casting direction and suppresses parameter increments that may lead to changes in the surface topology. This process is iterated until all vertices on the mesh satisfy the requirements. It outputs a triangular mesh surface that meets the global demolding angle requirements.

[0009] Furthermore, based on SDF calculation of the local cross-sectional thickness of the blade, the logic of inputting the triangular mesh surface into the thermodynamic model is as follows: Based on the zero isosurface of SDF, the local cross-sectional thickness at the vertices of the triangular mesh surface is calculated using the ray projection method, generating a thickness feature field corresponding to the vertices of the triangular mesh surface; the triangular mesh surface is then input into a thermodynamic model to simulate the spatiotemporal evolution of the temperature field during the casting process, thus obtaining the thermal state field. The obtained thermal state field and the corresponding thickness feature field are interpolated and aligned to the same grid resolution, and then input into the spatiotemporal feature extraction network to analyze the spatiotemporal evolution law under the thermodynamic-geometric coupling effect. The spatiotemporal feature extraction network outputs the spatial distribution of the probability of shrinkage defects in the propeller body.

[0010] Furthermore, the logic for outputting the spatial distribution of the probability of shrinkage defects in the propeller body is as follows: thermal field After bilinear interpolation resampling and reconstruction into a 3D tensor of size 100×100×50, the defect feature extraction operator... Defined as: ; in, Let p be the temperature gradient magnitude at the vertex p on the triangular mesh surface. Let p be the temperature gradient vector of the mesh vertex on the triangular mesh surface. Let be the second spatial derivative of the thermal field at grid vertex p along spatial direction i. These correspond to the x, y, and z coordinate axes, respectively. The kernels are 3×3×3, corresponding to the x, y, and z directions respectively; Represents a three-dimensional convolution operation. is a rectified linear unit used to introduce nonlinearity while preserving positive response, where p is the index of the mesh vertex on the triangular mesh surface; Through the fully connected layer Projection and calculation of the shrinkage cavity defect probability using the Sigmoid function: ; in, and These are the weight vector and bias scalar of the fully connected layer, respectively. Weight vector Transpose, output Let represent the probability of a shrinkage defect at the vertex p of the triangular mesh surface on the propeller body.

[0011] Furthermore, considering the spatial distribution of the shrinkage cavity defect probability and hydrodynamic performance, the logic for constructing the optimization objective function is as follows: For the local cross-sectional thickness at the mesh vertex p on the triangular mesh surface Based on its relationship with the critical thickness of thin walls Relationship allocation defects suppress weights : ; in, This is the critical thickness for thin-walled structures. This is the weight growth rate control coefficient, controlling... exist The steep rise in the region; for all conditions that meet the criteria thin-walled regions, Significantly amplify defect penalties; Construct the optimization objective function The calculation formula is as follows: ; in, Let be the set of all mesh vertices in the triangular mesh surface. The total number of grid vertices. To determine the hydrodynamic efficiency based on the current propeller design, Based on the baseline hydrodynamic efficiency, To balance the weights of defect suppression and efficiency preservation; The optimization objective function Minimization using gradient descent aims to simultaneously achieve: 1) targeted suppression of defects in thin-walled regions, i.e., reducing... 2) Relative loss of constrained hydrodynamic efficiency .

[0012] Furthermore, the logic for backpropagating the gradient of the objective function to the coordinates of the geometric control points is as follows: The geometry of the propeller blades is parameterized by a set of geometric control point coordinates, defined as follows: ,in This represents the three-dimensional coordinates of the e-th geometric control point, where e is the index of the three-dimensional coordinates of the geometric control point. The total number of internal three-dimensional coordinates of the set of geometric control point coordinates; Symbolic distance field It is a set of geometric control point coordinates The scalar field function is determined, and its zero isosurface ... The geometric surface of the propeller is defined; a triangular mesh surface is obtained by discrete sampling based on this zero isosurface, and the coordinates of the geometric control points are established by implicit function theorem regarding the position of the mesh vertex p. Gradient dependency: Optimize the objective function Decomposed into defect prediction items Hydrodynamic performance items Calculate the coordinates of the geometric control points respectively. Gradients and combinations: ; Defect prediction term gradient Calculated using the following chain rule: ; in, The weighted defect penalty coefficient at grid vertex p is... The sensitivity of the thermal-defect characteristic link, For geometric response function, This represents the sensitivity of thickness to heat conduction in the thermodynamic model. Calculate the geometric derivative of the ray projection thickness with respect to the SDF; Gradient of hydrodynamic performance terms Calculated using the differential CFD module: ; Based on gradient The geometric control point coordinates are updated using the gradient descent algorithm. .

[0013] Furthermore, the logic for iteratively updating the geometric control point coordinate set by repeating steps 1 to 3 is as follows: When the iteration terminates, the final set of geometric control point coordinates is obtained. and based on Reconstructing the symbolic distance field function ,extract The zero isosurface is used to generate a continuously differentiable CAD geometric model through a non-uniform rational B-spline surface fitting algorithm, and the fitting residuals satisfy... The output model format is the industry-standard BREP file; The iteration terminates when any of the following stopping conditions are met, and the final propeller geometry model is output: 1) The average porosity is reduced to below the target level: 2) The relative loss of hydrodynamic efficiency does not exceed the tolerance range, i.e. 3) Optimize the objective function in 5 consecutive iterations The improvement is less than 0.001, and the total number of iterations reaches 200. Before terminating the iteration, a final verification should be performed on the final generated triangular mesh surface, including: verifying the angle between the normal vector at all mesh vertices and the casting direction to ensure the global demolding angle. Verify the conformity of the surface geometry to hydrodynamic performance; generate a propeller geometric model that meets the demolding requirements and takes into account hydrodynamic performance, for use in subsequent detailed design and manufacturing processes.

[0014] The present invention also provides a machine learning-based ship propeller design optimization system, the system being used to execute the above-described machine learning-based ship propeller design optimization method, comprising: The surface construction module is used to construct a parametric surface based on the coordinate set of geometric control points of the ship propeller blades, and convert it into an initial triangular mesh surface. It calculates the angle between the normal vector of each vertex of the mesh and the casting direction, identifies vertices with angles less than the preset demolding angle threshold, and adjusts the coordinates of the geometric control points through a gradient optimization algorithm to drive the surface deformation until all vertices meet the demolding angle constraint, and finally generates a triangular mesh surface. The defect calculation module is used to calculate the local cross-sectional thickness of the blade based on SDF. It inputs the triangular mesh surface into the differential thermodynamic model to simulate the evolution of the thermal state field during the casting process. The thermal state field and the local cross-sectional thickness are input into the spatiotemporal feature extraction network to output the spatial distribution of the probability of shrinkage defects in the propeller body. The target optimization module is used to integrate the spatial distribution of the probability of shrinkage defects with hydrodynamic performance, construct the optimization objective function, and propagate the gradient of the optimization objective function from the thermal field through the triangular mesh surface and SDF to the coordinates of each geometric control point through the differential simulation link. Based on the gradient information, the optimization algorithm is used to update the coordinates of all geometric control points synchronously. The iterative update module is used to repeatedly execute steps 1 to 3, iteratively updating the geometric control point coordinate set until the probability of shrinkage defects in the entire domain does not exceed the preset safety threshold, the hydrodynamic performance loss is within the tolerance range, and the optimization objective function converges to a stable range. The loop terminates and outputs the propeller geometric model constructed based on the final geometric control point coordinate set.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention generates a mesh by extracting the SDF zero isosurface and calculating the angle between the normal and the casting direction. It introduces the demolding angle constraint in the early stage of optimization and uses the gradient algorithm to dynamically adjust the coordinates of the control points to drive the surface shape change. This fundamentally avoids the process defect of insufficient demolding angle in the early stage of design and overcomes the lag and passivity caused by the post-verification of manufacturing constraints in traditional methods. This invention realizes the gradient calculation of shrinkage defect probability with respect to local thickness and SDF through heat conduction simulation and spatiotemporal feature extraction network. Combined with implicit function theorem, it establishes explicit gradient correlation of SDF with control points, so that the gradient of the comprehensive objective function can be directly backpropagated from defect probability and efficiency index to geometric control points. This mechanism completely solves the bottleneck problem of gradient transmission break and inability to be updated synchronously between multidisciplinary analysis in the traditional propeller design process, and realizes synchronous optimization of hydrodynamic performance and casting quality in each iteration. This invention, through the deep integration of modeling and gradient propagation, enables propeller design to not only collaboratively handle conflicting objectives across multiple disciplines, but also significantly improves the convergence speed and stability of the optimization process. It avoids the local optima and computational redundancy problems commonly found in traditional trial-and-error optimization or surrogate model methods, thereby outputting a reliable design scheme that combines high performance and high manufacturability. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This is a line graph of the defect suppression weight-optimization objective function of this invention; Figure 3 This is a kite diagram of the defect suppression weight, shrinkage defect probability, and optimization objective function of this invention. Figure 4 The objective function for this invention is the current hydrodynamic probability bubble diagram. Figure 5 This is a curve showing the fitting of the defect suppression weights and the optimization objective function in this invention. Figure 6 This is a flowchart of the overall system modules of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0018] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0019] Example: Please see Figures 1-5 The present invention provides a technical solution: A machine learning-based method for optimizing ship propeller design, comprising the following steps: Step 1: Construct a parametric surface based on the coordinate set of the geometric control points of the ship propeller blades, and convert it into an initial triangular mesh surface. Calculate the angle between the normal vector of each vertex of the mesh and the casting direction, identify vertices with angles less than the preset demolding angle threshold, and adjust the coordinates of the geometric control points through a gradient optimization algorithm to drive the surface deformation until all vertices meet the demolding angle constraint, and finally generate a triangular mesh surface. The logic for constructing a parametric surface based on the coordinate set of geometric control points of a ship's propeller blade is as follows: An explicit parameterized surface for the propeller blade is constructed based on the geometric control point coordinate set Q, and the corresponding signed distance field is established. ,in The zero isosurface is the implicit geometric expression of this parameterized surface; By using mathematical methods such as NURBS and B-splines to connect, interpolate, and smoothly unfold the coordinates of these geometric control points into a complete surface, an explicit parametric surface is obtained. Its explicitness is reflected in the fact that the points on the surface can be directly expressed using parametric equations; its parametric characteristics mean that by adjusting the position of the control points in Q, the shape of the entire surface can be directly and intuitively changed. SDF transforms an explicit surface into an implicit scalar field, where any point in space... The value represents the shortest distance from the point to the propeller surface. It is agreed that the distance is negative when the point is inside the object and positive when it is outside. The isosurface with SDF equal to zero isosurface, which accurately restores the original propeller surface. The advantage of this implicit expression is that it naturally avoids complex problems such as self-intersection and cracks that may occur in explicit representation, and it is very convenient for topological transformation and Boolean operations. The above is obtained by isosurface extraction algorithm The zero isosurface is converted into an initial triangular mesh surface. The normal vector at each vertex of the initial triangular mesh surface is calculated. The normal vector is determined by the gradient direction of the SDF at the vertex. The casting direction refers to the relative motion direction when the mold is opened and the casting is removed after the molten metal is poured into the mold and solidifies into propeller blades. It is emphasized that the SDF is uniquely determined by the control point set Q; The initial triangular mesh surface is generated from the zero isosurface of the SDF by isosurface extraction algorithms, such as the classic Marching Cubes or its improved algorithms. This step is the key to discretizing the continuous mathematical expression into a patch model that can be directly processed and displayed by the computer. Calculating the normal vector at each vertex of the mesh is the basis for subsequent determination of the demolding angle. Here, we take advantage of an excellent feature of the SDF: the direction of its gradient vector at any point is the normal direction of the isosurface at that point, and it is a unit vector. The casting direction is a core concept derived from actual production processes. It defines the direction in which the mold or casting is moved to remove the casting after it has solidified in the mold. Any curved surface that is parallel to this direction or has too small an angle with it will cause severe friction and scratching with the mold during the demolding process, resulting in the part being unable to be removed or its surface quality being damaged. Therefore, it is necessary to calculate the angle between the normal vector at each grid vertex and this fixed casting direction. Point-by-point comparison of the angle between the normal vector of each vertex on the initial triangular mesh surface and the casting direction. Identify all that meet the requirements The vertex region, in which The minimum demolding angle threshold is set separately for different regions of the propeller blade: the minimum demolding angle for the pressure surface region of the propeller blade is... The minimum demolding angle of the blade suction surface area is The minimum draft angle for the hub connection area is... And satisfy the constraints. ; The normal vector is the core geometric quantity for determining the demolding angle. For discrete triangular meshes, calculating the normal vector usually requires averaging the normals of adjacent faces. This method is prone to errors on low-quality meshes. The method described above utilizes a key mathematical property of SDF: the direction of the gradient vector of SDF at a certain point is the direction of the normal of the isosurface at that point, and it is a unit vector. Therefore, directly calculating the SDF gradient at the vertex to obtain the normal vector is an extremely accurate, stable, and efficient method that is not affected by mesh quality. The hub connection area typically has a complex structure and significant thickness variations, resulting in the greatest demolding resistance. Therefore, it is assigned the most stringent maximum demolding angle threshold. As the main working surface for propelling water flow, the blade pressure surface requires high geometric fidelity, but the demolding difficulty is moderate, and the threshold is [not specified]. The threshold is relatively loose, while the process constraints on the suction surface are usually the lowest, hence the threshold... Most lenient; For the region where the included angle does not reach the demolding angle threshold: the signed distance field of the parameterized surface with the geometric control point coordinate set Q as the independent variable. This involves calculating the demolding angle violation degree for each vertex and transferring this violation degree's sensitivity with respect to the mesh vertices back to Q along the mapping to obtain the manufacturing constraint gradient. This gradient is then transferred to the geometric control point coordinates via the signed distance field. Based on the manufacturing constraint gradient, Q is updated using constrained numerical optimization to drive local deformation of the parameterized surface. This constrained numerical optimization ensures the reasonableness of the deformation in the casting direction and suppresses parameter increments that may lead to changes in the surface topology. This process is iterated until all vertices on the mesh satisfy the requirements. It outputs a triangular mesh surface that meets the global demolding angle requirements; The qualitative problem of not meeting the requirements can be transformed into a quantifiable mathematical objective; the degree of violation can be simply defined as... This function means if the included angle The requirement has been met, i.e., greater than or equal to If the condition is met, the violation rate is 0, and no penalty is required; if not, the violation rate is positive, and the larger the difference, the higher the violation rate. This function provides a clear objective for optimization: to minimize the total violation rate of all vertices. Sensitivity refers to how sensitive the change in the violation degree of a vertex is to the geometric changes of the vertex itself. Mapping refers to a complete calculation chain from geometric control point coordinates → SDF → mesh vertex p → normal vector → included angle → violation degree. Through the chain rule, the algorithm can automatically and accurately deduce from the violation degree sensitivity of the vertex how each geometric control point coordinate should be moved and by how much to move in order to most effectively reduce the total violation degree. The direction of this deduction is to create constraint gradients. This is equivalent to the computer automatically performing a perfect sensitivity analysis and finding the optimal modification path. The geometric control point coordinates are fine-tuned based on the gradient calculated in the previous step. This is an iterative process: each time, the geometric control point coordinates are fine-tuned one point → the SDF and mesh vertices are updated → the violation degree and gradient are recalculated → fine-tuning is done again. Constraints and local deformations are key. Optimization is not a rapid and aggressive process, but a controlled and precise one. It only moves the control points that are most effective in solving the demolding problem, so that the deformation mainly occurs near the problem area, and the original design shape of the rest of the propeller is preserved to the greatest extent. The significance of "the constrained numerical optimization used to ensure the rationality of deformation in the casting direction and suppress parameter increments that may lead to changes in surface topology" lies in ensuring the rationality of deformation in the casting direction. This means that the optimization will prioritize guiding the surface to stretch or adjust along the direction that is conducive to demolding, i.e., the direction in which the mold opens, rather than doing useless or even harmful deformation in other directions. Topology refers to the basic connection relationship of an object, such as how many blades there are and whether there are holes on the blades. This rule prohibits the optimization process from changing the topology. For example, it does not allow two blades to be fused together in order to increase the demolding angle, or to tear a hole in a closed surface. It ensures that the final result is still a usable propeller. The above process is repeated until it is detected that each point fully meets the demolding angle requirements of its area. The final output is no longer just a design model, but a product model that has passed manufacturability certification and is designed to be manufactured.

[0020] Step 2: Calculate the local cross-sectional thickness of the blade based on SDF, input the triangular mesh surface into the differential thermodynamic model to simulate the evolution of the thermal state field during the casting process, and input the thermal state field and the local cross-sectional thickness into the spatiotemporal feature extraction network to output the spatial distribution of the probability of shrinkage defects in the propeller body. The logic for calculating the local cross-sectional thickness of the blade based on SDF, and inputting the triangular mesh surface into the thermodynamic model, is as follows: Based on the zero isosurface of SDF, the local cross-sectional thickness at the vertices of the triangular mesh surface is calculated using the ray projection method, generating a thickness feature field corresponding to the vertices of the triangular mesh surface; the triangular mesh surface is then input into a thermodynamic model to simulate the spatiotemporal evolution of the temperature field during the casting process, thus obtaining the thermal state field. At each vertex p of the mesh, a ray is emitted along its normal direction (both positive and negative directions). This ray intersects the zero isosurface of the SDF (i.e., the other side surface of the propeller). The distance between the mesh vertex p and the intersection point is calculated. This distance is the local cross-sectional thickness at that point. A thickness value is calculated for each mesh vertex, forming a thickness feature field covering the entire surface of the propeller. The geometric model of the propeller (the triangular mesh defines the boundary of the computational domain) is input into a simplified computational fluid dynamics / heat transfer model. This model solves the heat conduction equation and simulates the temperature change at each point inside the propeller at different times during the entire process from casting to complete solidification. The thermal state field records the temperature history of each mesh vertex p at each moment. The obtained thermal state field and the corresponding thickness feature field are interpolated and aligned to the same grid resolution, and then input into the spatiotemporal feature extraction network to analyze the spatiotemporal evolution law under the thermodynamic-geometric coupling effect. The spatiotemporal feature extraction network outputs the spatial distribution of the probability of shrinkage defects in the propeller body. To prepare standardized input data for the neural network, the thermal field (from the volume mesh) and the thickness field (from the surface mesh) typically have different spatial resolutions and data formats. Through interpolation techniques, such as bilinear interpolation, the thermal field and the thickness field are resampled onto the same regular 3D mesh, i.e., a 100x100x50 mesh, ensuring that each mesh cell has both temperature and thickness values. Defects are the result of thermal-geometric coupling. The temperature field alone cannot determine whether a location is thick or thin; the thickness field alone cannot determine how fast it cools. Both must be combined so that the network can learn the complex pattern that defects are prone to occur in thick areas with slow cooling. 100x100x50 divides the physical space into 100×100×50 cubic / cubic voxels, which is a three-dimensional grid size. 100 (x-direction) means that the physical domain is divided into 100 units on the x-axis. The second 100 (y-direction) is the same, and 50 (z-direction) means that the z-direction is divided into 50 layers. The spatiotemporal feature extraction network adopts a lightweight architecture guided by physical priors, and its specific components are as follows: The input layer receives a three-dimensional thermal state field tensor with a size of 100×100×50. First, a feature extraction module calculates the defect feature tensor. This module uses three independent 3×3×3 three-dimensional convolutional kernels to process temperature field information in the x, y, and z spatial directions respectively, and uses ReLU as the activation function. Then, the resulting feature tensor is processed. The input is a fully connected layer, and the output is the probability of shrinkage defects after passing through a sigmoid activation function. ; The logic for outputting the spatial distribution of the probability of shrinkage defects in the propeller body is as follows: thermal field After bilinear interpolation resampling and reconstruction into a 3D tensor of size 100×100×50, the defect feature extraction operator... Defined as: ; in, Let p be the temperature gradient magnitude at the vertex p on the triangular mesh surface. Let p be the temperature gradient vector of the mesh vertex on the triangular mesh surface. Let be the second spatial derivative of the thermal field at grid vertex p along spatial direction i. These correspond to the x, y, and z coordinate axes, respectively. The kernels are 3×3×3, corresponding to the x, y, and z directions respectively; Represents a three-dimensional convolution operation. is a rectified linear unit used to introduce nonlinearity while preserving positive response, where p is the index of the mesh vertex on the triangular mesh surface; The rate of temperature change at point p reflects the degree of drastic change, i.e., the cooling rate, indicating how quickly heat is dissipated at that point. The larger the value, the more drastic the temperature change at that point, the faster the cooling rate, and the less likely shrinkage cavities will occur. Therefore, a larger value should tend to reduce the probability of defects. The curvature of the temperature gradient magnitude at grid vertex p in the i direction indicates whether the point is a local high-temperature region. A positive value indicates a local bulge (high-temperature point), and a negative value indicates a local depression (low-temperature point). The larger the positive value, the more obvious the isolated high-temperature point is. The larger the positive value, the greater the possibility of forming a hot spot and the easier it is to produce shrinkage cavities. This reflects the coupling effect of cooling rate and thermal intensity, indicating the severity of a point that is both a thermal hotspot and slow to cool; if a point is a strong thermal hotspot... (It is a large positive value), but it cools down very quickly ( The product may not be large, and the defect risk may not be the highest, especially if a point is a strong hot spot ( (large positive value), and cools down very slowly ( (If the product is very small, the product will be a large positive value, which perfectly indicates the most dangerous defect area. This product term is a key physical feature for identifying defects.) Using three convolution kernels in different directions The hot spot features in the three directions are processed separately and then summed to extract the hot spot features in each direction in three-dimensional space. The convolution operation can fuse the information of adjacent points, making the features more robust. The ReLU function retains positive values ​​and discards negative values. Only those features judged as potentially dangerous (i.e., the product term is positive) are retained and passed to the next layer. Negative values, such as features of rapidly cooling areas or non-hot spot areas, are suppressed to 0. This introduces nonlinearity and makes the network focus on "bad" signals. In summary, It is a high-dimensional feature vector, where the value in each dimension reflects the probability that a grid vertex p and its neighborhood are dangerous hotspots. The larger the value, the higher the risk of defects in the area; Through the fully connected layer Projection and calculation of the shrinkage cavity defect probability using the Sigmoid function: ; in, and These are the weight vector and bias scalar of the fully connected layer, respectively. Weight vector Transpose, output Let p represent the probability of a shrinkage defect at the vertex p of the triangular mesh surface on the propeller body; This formula extracts the complex physical features from the previous step. Mapped to a simple scalar with a clear probabilistic meaning, the sigmoid function compresses a real number of any range to a scalar. The values ​​between these two points conform to the definition of probability. Reflecting all defect characteristics The weighted composite score, weight It is obtained through network training and determines the importance of different features to the final decision; the higher the comprehensive score, the more the sum of all features supports the judgment that "this point is defective"; Sigmoid function output This reflects the probability of defect occurrence calculated based on the comprehensive score, for example... This indicates that the model predicts there is a 95% probability that a shrinkage hole will occur at this point; The larger the value, the closer the output of the Sigmoid function is to 1, thus increasing the defect probability. The higher, The smaller (more negative) the value, the closer the output of the Sigmoid function is to 0, thus increasing the defect probability. The lower.

[0021] Step 3: Combining the spatial distribution of the shrinkage cavity defect probability with hydrodynamic performance, construct an optimization objective function. Through differential simulation link, propagate the gradient of the optimization objective function from the thermal state field through the triangular mesh surface and SDF back to the coordinates of each geometric control point. Based on the gradient information, use the optimization algorithm to synchronously update the coordinates of all geometric control points. Based on the spatial distribution of the probability of shrinkage cavities and hydrodynamic performance, the logic for constructing the optimization objective function is as follows: For the local cross-sectional thickness at the mesh vertex p on the triangular mesh surface Based on its relationship with the critical thickness of thin walls Relationship allocation defects suppress weights : ; in, This is the critical thickness for thin-walled structures. This is the weight growth rate control coefficient, controlling... exist The steep rise in the region; for all conditions that meet the criteria thin-walled regions, Significantly amplify defect penalties; This reflects the degree to which the mesh vertex p needs special attention due to insufficient thickness, indicating the severity and sensitivity of the defect risk at that point. The larger the value, the thinner the region containing that point. much smaller During the optimization process, the probability of defects in this area is reduced. The greater the urgency and importance, the higher the priority. This difference measures the gap between the current thickness and the safe thickness; the larger the difference, the thinner the thickness at that point. Much larger (That is, for thick areas) It is a very large negative value. It becomes a huge number, leading to A value close to 0 means that the penalty for defects in thick areas is significantly reduced. when much smaller (i.e., for thin-walled regions) It is a very large positive value. Approaching 0, resulting in A value close to 1 means that the defect penalty in the thin-walled region is fully retained or even amplified. Control the steepness of the change in weights from 0 to 1. The larger the value, the more drastic the change, meaning the more sensitive the system is to changes below a critical thickness. Construct the optimization objective function The calculation formula is as follows: ; in, Let be the set of all mesh vertices in the triangular mesh surface. The total number of grid vertices. To determine the hydrodynamic efficiency based on the current propeller design, Based on the baseline hydrodynamic efficiency, To balance the weights of defect suppression and efficiency preservation; This reflects the overall dissatisfaction with the current propeller design. The higher the value, the higher the risk of defects, the greater the efficiency loss, or both. It reflects the weighted average defect risk of the entire propeller. The higher the value, the higher the overall defect risk, especially the risk in thin-walled areas. Reflects current efficiency relative to baseline efficiency The relative loss rate The larger the value, the greater the efficiency loss; the larger the value, the more severe the degradation of hydrodynamic performance relative to the original design. The higher the setting, the more aggressively the optimization algorithm will strive to maintain efficiency, potentially even allowing for a slightly higher risk of defects. The smaller the setting, the more aggressively the optimization algorithm will reduce the risk of defects, and may even accept some efficiency loss. It is a current, dynamic performance indicator, and the object being tuned in the optimization process. It is a fixed, static benchmark value, a scale for measuring performance changes; This represents the hydrodynamic efficiency value calculated by a hydrodynamic performance evaluation model based on the triangular mesh surface generated from the current geometric control point coordinate set Q. In each optimization iteration, the process is as follows: Define the geometry using the current geometric control point coordinate set Q, and generate the corresponding triangular mesh surface using this geometry; input this triangular mesh surface into a validated hydrodynamic performance evaluation module, which can be a high-fidelity computational fluid dynamics solver that calculates the efficiency by numerically simulating the thrust and torque of a propeller at a specific advance velocity. ; It is a variable whose value changes dynamically with the update of the geometric control point coordinate set Q and the change of geometry; it is the output feedback of the optimization process. It is a fixed reference value, representing the hydrodynamic efficiency under initial design or a certain accepted design state; the baseline hydrodynamic efficiency. The value is set to 0.75. This value is the hydrodynamic efficiency assessment value of the initial propeller design model, and its main function is to account for the efficiency loss term. Normalization is performed, which makes the loss term Becoming a dimensionless relative value is easier to understand, and is related to the defective term. (It is also a scalar near 0 to 1) It matches on a numerical scale, making it easy to weigh factors. Without this normalization, it is impossible to achieve an effective balance between two competing objectives. Will need to be based on Making huge adjustments to the absolute value range is very inconvenient; The optimization objective function Minimization using gradient descent aims to simultaneously achieve: 1) targeted suppression of defects in thin-walled regions, i.e., reducing... 2) Relative loss of constrained hydrodynamic efficiency ; Table 1 shows some of the data numbers and specific data for the optimization objective function.

[0022] Table 1

[0023] Analysis of the data revealed a certain correlation between different characteristic parameters. For example, the data showed that the synergistic effect of defect suppression weight and shrinkage defect probability significantly influenced the optimization objective function value. When both defect suppression weight and shrinkage defect probability were at a high level, such as in sample number 6 where the defect suppression weight was 0.9 and the shrinkage defect probability was 0.6, the optimization objective function value reached 0.480. However, in sample number 7, where the defect suppression weight was low and the shrinkage defect probability was high, although the shrinkage defect probability reached 0.7, the optimization objective function value was relatively low at 0.093 because the defect suppression weight was only 0.1. This indicates that in the manufacturing process, focusing on suppressing high-defect-risk areas can effectively improve overall quality performance. When analyzing the relationship between hydrodynamic efficiency and the objective function value, the objective function value gradually decreases as hydrodynamic efficiency increases. For example, in sample number 3, the hydrodynamic efficiency is 0.76, and the corresponding objective function value is 0.307. However, in sample number 9, when the hydrodynamic efficiency drops to 0.70, the objective function value increases significantly to 0.627. This indicates that higher propulsion efficiency helps to reduce the overall objective function value. However, it should be noted that when the surface quality risk is high, even if the hydrodynamic efficiency is good, the objective function value may still be at a high level. Further observation revealed that when the surface quality risk index, i.e., the product of the defect suppression weight and the probability of shrinkage defects, is maintained at a low level, even if the hydrodynamic efficiency is mediocre, the optimization objective function value can still be kept within a relatively ideal range. For example, in sample number 1, the surface quality risk is low, the hydrodynamic efficiency is 0.72, and the optimization objective function value is only 0.063. This indicates that in the propeller design process, it is necessary to comprehensively consider the balance between surface quality characteristics and hydrodynamic performance, and to achieve the overall goal of controlling defect risk while ensuring hydrodynamic efficiency by optimizing the distribution of geometric feature control points.

[0024] The logic for backpropagating the gradient of the objective function to the coordinates of the geometric control points is as follows: The geometry of the propeller blades is parameterized by a set of geometric control point coordinates, defined as follows: ,in This represents the three-dimensional coordinates of the e-th geometric control point, where e is the index of the three-dimensional coordinates of the geometric control point. The total number of internal three-dimensional coordinates of the set of geometric control point coordinates; Symbolic distance field It is a set of geometric control point coordinates The scalar field function is determined, and its zero isosurface ... The geometric surface of the propeller is defined; a triangular mesh surface is obtained by discrete sampling based on this zero isosurface, and the coordinates of the geometric control points are established by implicit function theorem regarding the position of the mesh vertex p. Gradient dependency: Optimize the objective function Decomposed into defect prediction items Hydrodynamic performance items Calculate the coordinates of the geometric control points respectively. Gradients and combinations: ; The total gradient consists of two parts: the gradient of the defect term and the gradient of the hydrodynamic performance term. This indicates the direction of control point movement and also considers how to reduce defects. and how to improve efficiency , This also serves as a trade-off, amplifying or diminishing the influence of the performance gradient; Defect prediction term gradient Calculated using the following chain rule: ; in, The weighted defect penalty coefficient at grid vertex p is... The sensitivity of the thermal-defect characteristic link, For geometric response function, This represents the sensitivity of thickness to heat conduction in the thermodynamic model. Calculate the geometric derivative of the ray projection thickness with respect to the SDF; Derived from the objective function itself, it represents the proportion of the contribution of mesh vertex p to the total defect cost. The larger the value, the stronger the gradient signal at this point; This link answers the question, "How would changing the temperature history at this point affect the final defect prediction probability?" For defect probability pairs Sensitivity, representing the characteristics of a neural network For each slight change, the probability of it ultimately being judged as a defect... How much will it change? Features thermal field The sensitivity represents the extraction of [value] for each point change in the thermal state field. How much will it change? This refers to the sensitivity of the thermal field to local thickness, which is a core output of differentiable thermodynamic models. It precisely answers the question of "how would the cooling process be affected if this point became thicker (or thinner)?" Increased thickness typically leads to slower cooling. It is easier to form hot spots; This link answers the question of "coordinates of moving geometric control points". "How will it change the thickness at mesh vertex p?", it contains two paths: 1) Shape changes directly lead to thickness changes; control point movement → SDF change → ray penetration path change → thickness change; 2) Vertex movement causes indirect changes in thickness. Control point movement → mesh vertex p moves slightly → thickness is evaluated at the new position; The intermediate sensitivities in the gradient propagation path include, but are not limited to, the following: , The calculation relies on integrating modules such as geometric modeling, physical simulation, and defect prediction into a differentiable programming framework, thus forming an end-to-end differentiable computational graph. In this computational graph, the aforementioned sensitivity is automatically calculated by the framework's automatic differentiation function during backpropagation. Specifically, by implementing a differentiable thermodynamic model, the temperature field is ensured. For local thickness Differentiability; by implementing a differentiable ray casting algorithm, local thickness is ensured. For the symbolic distance field Differentiability; Gradient of hydrodynamic performance terms Calculated using the differential CFD module: ; Indicates the current hydrodynamic efficiency For each control point The motion sensitivity calculates "how much the propeller efficiency will change if I push this control point a little in a certain direction." This gradient field is usually very complex, containing all the information about the fluid's interaction with complex geometry; the negative sign is to maximize efficiency. However, the optimization objective is to minimize hydrodynamic efficiency Increase will lead to Reduce, thus Decrease, therefore gradient The direction is to improve efficiency, and it can be directly used to reduce... This can be achieved through gradient descent updates; The implementation of the differentiable thermodynamic model is based on a computational framework with automatic differentiation capabilities. In this implementation, the computational domain is discretized into a grid, with the temperature of each grid cell as a variable. Numerical solution operations, such as heat flow calculations based on Fourier's law and time integration stepping, are all implemented as differentiable operations (such as tensor operations) within the framework. Thus, the entire process from inputs, such as boundary geometry and material properties, to output (temperature field) constitutes a differentiable computational graph. The framework can automatically calculate the gradient of the output with respect to the input, thereby obtaining the... Isosensitivity; Gradient-based The geometric control point coordinates are updated using the gradient descent algorithm. The specific steps include: Let the global gradient vector be: ; in, This is the transpose symbol; it provides a global overview of the optimization directions for all control points, concatenating the gradients of all control points (each a three-dimensional vector) into a long column vector. This vector has a dimension of 3n×1 (n points, each with three coordinate directions: x, y, and z). To perform subsequent global gradient clipping, the optimization process needs to consider the update pace of all control points simultaneously to avoid excessively large update amplitudes at some points that could compromise the overall optimization stability. Therefore, the norm of this global vector needs to be calculated. It is used to measure the magnitude of the total gradient in the current optimization step; The geometric control point coordinates are updated using the gradient descent algorithm with momentum: This indicates that instead of using the most basic gradient descent method, two advanced optimization techniques, momentum and gradient clipping, were employed to accelerate convergence and improve stability. These are the core ideas of modern deep learning optimizers, such as Adam and RMSProp. ; in, For learning rate, The momentum coefficient, The gradient clipping threshold, For the number of iterations, L2 norm, also known as Euclidean norm, is the square root of the sum of the squares of all gradient components. It measures the total length or magnitude of the vector formed by the gradients of all control points. It is the previous iteration step ( In the step, the coordinates of the geometric control points The update vector contains not only the gradient direction from the previous step, but also the accumulated update inertia. The momentum term determines how much of the previous update is retained, which can be understood as the weight of inertia. In a stable optimization direction, such as a continuous downhill slope, the momentum term will cause the update to accumulate continuously, rolling faster and faster, thus greatly accelerating convergence. When the optimization path is a narrow valley, the gradient direction will oscillate back and forth. The momentum term is like a damper. Due to inertia, it will weaken the oscillations perpendicular to the valley direction, making it move more smoothly along the valley direction. The step size of each iteration is controlled, usually much smaller than 1, such as 0.001 or 0.0001. If the learning rate is too large, the update step will be too large, which may cause oscillations around the optimum or even divergence; if the learning rate is too small, the convergence speed will be extremely slow, or even get stuck in a local optimum. It is a very small positive number, a safety valve used to prevent division by zero. To obtain and The maximum value in means if Because the result is calculated as 0 (or extremely small) for some reason, the denominator will not be zero, thus avoiding numerical calculation errors; In complex optimization problems, the gradient magnitudes of different iteration steps may vary greatly. Gradient explosion at a certain step can lead to excessively large update steps, disrupting the optimization process. Pruning can effectively prevent this situation, ensuring that all control points are updated at a relatively consistent pace, avoiding some points from "running too far" due to large gradients, thus disrupting the geometric consistency. The calculated update vector (It already contains momentum information and clipping processing) and is added to the current control point coordinates to obtain the new coordinates for the next iteration.

[0025] Step 4: Repeat steps 1 to 3, iteratively updating the geometric control point coordinate set until the probability of shrinkage defects in the entire domain does not exceed the preset safety threshold, the hydrodynamic performance loss is within the tolerance range, and the optimization objective function converges to a stable range. Terminate the loop and output the propeller geometric model constructed based on the final geometric control point coordinate set. The logic for iteratively updating the geometric control point coordinate set by repeating steps 1 to 3 is as follows: When the iteration terminates, the final set of geometric control point coordinates is obtained. and based on Reconstructing the symbolic distance field function ,extract The zero isosurface is used to generate a continuously differentiable CAD geometric model through a non-uniform rational B-spline surface fitting algorithm, and the fitting residuals satisfy... The output model format is the industry-standard BREP file; The optimization process uses discrete triangular meshes and implicit SDF, but industrial design and manufacturing require higher-order, smoother continuous surface models. NURBS is the standard language in the CAD field. This algorithm will reconstruct smooth, parametric surfaces from discrete mesh points. Such surfaces are continuously differentiable, meaning there are no sharp points or edges, which is crucial for fluid dynamics performance and CNC machining. This requirement ensures a high degree of consistency between the fitted NURBS surface and the optimized SDF zero isosurface (i.e., the ideal design shape), with minimal residuals. This indicates that the CAD model perfectly reproduces the optimized design results without introducing shape errors. BREP (Boundary Representation) is the mainstream format for describing solid models. It can be read by all CAD software, such as CATIA, SolidWorks, NX and CAE / CAM software. Outputting BREP files means that the optimized design results can be directly used to: add machining allowances, labels, etc., design mold cores and cavities based on this model, generate G-code to drive CNC machine tools, and perform more refined finite element analysis, etc. The iteration terminates when any of the following stopping conditions are met, and the final propeller geometry model is output: 1) The average porosity is reduced to below the target level: This reflects the average defect risk level of the entire propeller surface. It averages the predicted probabilities at all vertices to obtain a macroscopic quality index, which indicates the overall casting quality of the design. The larger the value, the higher the overall probability of shrinkage defects in the entire casting and the worse the average quality. Less than 0.005 is a very strict quality target, which means that on average, only 5 points out of every 1000 points are considered to be at risk of defects. This is equivalent to setting a high standard that more than 99.5% of the area is safe. 2) The relative loss of hydrodynamic efficiency does not exceed the tolerance range, i.e. This reflects the percentage change in hydrodynamic performance of the current design relative to the baseline design. It indicates the performance cost incurred to improve manufacturability; a higher value indicates a greater performance loss. A value of 0.01 indicates a 1% efficiency loss. The lower, The smaller the ratio, the better. The greater the difference, the greater the relative performance loss; less than 0.005 is a performance protection tolerance that limits the performance loss to within 0.5%, which means that the optimized design efficiency must not be lower than 99.5% of the baseline efficiency. This condition ensures that the optimization process will not excessively sacrifice the core function of the propeller - propulsion efficiency in pursuit of ultimate manufacturability. 3) Comprehensive optimization of the objective function in 5 consecutive iterations The improvement is less than 0.001. 4) The total number of iterations reaches 200, which reflects the convergence state of the optimization process. When continuous iterations can no longer significantly reduce the objective function value, it indicates that the algorithm has found a (possibly local) optimal solution, indicating that the optimization process has "squeezed out" all the potential under the current design framework, and continuing to iterate will yield little benefit. Less than 0.001 is a convergence accuracy indicator. It requires that the value of the optimization objective function decreases very little (less than 0.001) in each of the 5 consecutive iterations, indicating that the optimization process has stabilized. "5 consecutive iterations" is a robust design to prevent premature termination. A small improvement in a single iteration may be due to random fluctuations, but a small improvement in 5 consecutive iterations strongly indicates that convergence has occurred. Before terminating the iteration, a final verification should be performed on the final generated triangular mesh surface, including: verifying the angle between the normal vector at all mesh vertices and the casting direction to ensure the global demolding angle. Verify the conformity of the surface geometry to the hydrodynamic performance; Generate a propeller geometric model that meets demolding requirements and takes into account hydrodynamic performance, for use in subsequent detailed design and manufacturing processes.

[0026] Please see Figure 6 The present invention also provides a machine learning-based ship propeller design optimization system, the system being used to execute the above-described machine learning-based ship propeller design optimization method, comprising: The surface construction module is used to construct a parametric surface based on the coordinate set of geometric control points of the ship propeller blades, and convert it into an initial triangular mesh surface. It calculates the angle between the normal vector of each vertex of the mesh and the casting direction, identifies vertices with angles less than the preset demolding angle threshold, and adjusts the coordinates of the geometric control points through a gradient optimization algorithm to drive the surface deformation until all vertices meet the demolding angle constraint, and finally generates a triangular mesh surface. The defect calculation module is used to calculate the local cross-sectional thickness of the blade based on SDF. It inputs the triangular mesh surface into the differential thermodynamic model to simulate the evolution of the thermal state field during the casting process. The thermal state field and the local cross-sectional thickness are input into the spatiotemporal feature extraction network to output the spatial distribution of the probability of shrinkage defects in the propeller body. The target optimization module is used to integrate the spatial distribution of the probability of shrinkage defects with hydrodynamic performance, construct the optimization objective function, and propagate the gradient of the optimization objective function from the thermal field through the triangular mesh surface and SDF to the coordinates of each geometric control point through the differential simulation link. Based on the gradient information, the optimization algorithm is used to update the coordinates of all geometric control points synchronously. The iterative update module is used to repeatedly execute steps 1 to 3, iteratively updating the geometric control point coordinate set until the probability of shrinkage defects in the entire domain does not exceed the preset safety threshold, the hydrodynamic performance loss is within the tolerance range, and the optimization objective function converges to a stable range. The loop terminates and outputs the propeller geometric model constructed based on the final geometric control point coordinate set.

[0027] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0028] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0029] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0030] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A machine learning-based method for optimizing ship propeller design, characterized in that, The specific steps include: Step 1: Construct a parametric surface based on the coordinate set of the geometric control points of the ship propeller blades, and convert it into an initial triangular mesh surface. Calculate the angle between the normal vector of each vertex of the mesh and the casting direction, identify vertices with angles less than the preset demolding angle threshold, and adjust the coordinates of the geometric control points through a gradient optimization algorithm to drive the surface deformation until all vertices meet the demolding angle constraint, and finally generate a triangular mesh surface. Step 2: Calculate the local cross-sectional thickness of the blade based on SDF, input the triangular mesh surface into the differential thermodynamic model to simulate the evolution of the thermal state field during the casting process, and input the thermal state field and the local cross-sectional thickness into the spatiotemporal feature extraction network to output the spatial distribution of the probability of shrinkage defects in the propeller body. Step 3: Combining the spatial distribution of the shrinkage cavity defect probability with hydrodynamic performance, construct an optimization objective function. Through differential simulation link, propagate the gradient of the optimization objective function from the thermal state field through the triangular mesh surface and SDF back to the coordinates of each geometric control point. Based on the gradient information, use the optimization algorithm to synchronously update the coordinates of all geometric control points. Step 4: Repeat steps 1 to 3, iteratively updating the geometric control point coordinate set until the probability of shrinkage defects in the entire domain does not exceed the preset safety threshold, the hydrodynamic performance loss is within the tolerance range, and the optimization objective function converges to a stable range. Terminate the loop and output the propeller geometric model constructed based on the final geometric control point coordinate set.

2. The machine learning-based ship propeller design optimization method according to claim 1, characterized in that: The logic for constructing a parametric surface based on the coordinate set of geometric control points of a ship's propeller blade is as follows: An explicit parameterized surface for the propeller blade is constructed based on the geometric control point coordinate set Q, and the corresponding signed distance field is established. ,in The zero isosurface is the implicit geometric expression of this parameterized surface; The above is obtained by using an isosurface extraction algorithm. The zero isosurface is converted into an initial triangular mesh surface. The normal vector at each vertex of the initial triangular mesh surface is calculated. The normal vector is determined by the gradient direction of the SDF at the vertex. The casting direction refers to the relative motion direction when the mold is opened and the casting is taken out after the molten metal is injected into the mold and solidified into the propeller blade. Point-by-point comparison of the angle between the normal vector of each vertex on the initial triangular mesh surface and the casting direction. Identify all that meet the requirements The vertex, of which The minimum demolding angle threshold is set separately for different regions of the propeller blade: the minimum demolding angle for the pressure surface region of the propeller blade is... ; The minimum demolding angle of the blade suction surface area is The minimum draft angle for the hub-and-sprocket connection area is... And satisfy the constraints. ; For the region where the included angle does not reach the demolding angle threshold: the signed distance field of the parameterized surface with the geometric control point coordinate set Q as the independent variable. This involves calculating the demolding angle violation degree for each vertex and transferring this violation degree's sensitivity with respect to the mesh vertices back to Q along the mapping to obtain the manufacturing constraint gradient. This gradient is then transferred to the geometric control point coordinates via the signed distance field. Based on the manufacturing constraint gradient, Q is updated using constrained numerical optimization to drive local deformation of the parameterized surface. This constrained numerical optimization ensures the reasonableness of the deformation in the casting direction and suppresses parameter increments that may lead to changes in the surface topology. This process is iterated until all vertices on the mesh satisfy the requirements. It outputs a triangular mesh surface that meets the global demolding angle requirements.

3. The machine learning-based ship propeller design optimization method according to claim 2, characterized in that: The logic for calculating the local cross-sectional thickness of the blade based on SDF, and inputting the triangular mesh surface into the thermodynamic model, is as follows: Based on the zero isosurface of SDF, the local cross-sectional thickness at the vertices of the triangular mesh surface is calculated using the ray projection method, generating a thickness feature field corresponding to the vertices of the triangular mesh surface; the triangular mesh surface is then input into a thermodynamic model to simulate the spatiotemporal evolution of the temperature field during the casting process, thus obtaining the thermal state field. The obtained thermal state field and the corresponding thickness feature field are interpolated and aligned to the same grid resolution, and then input into the spatiotemporal feature extraction network to analyze the spatiotemporal evolution law under the thermodynamic-geometric coupling effect. The spatiotemporal feature extraction network outputs the spatial distribution of the probability of shrinkage defects in the propeller body.

4. The machine learning-based ship propeller design optimization method according to claim 3, characterized in that: The logic for outputting the spatial distribution of the probability of shrinkage defects in the propeller body is as follows: thermal field After bilinear interpolation resampling and reconstruction into a 3D tensor of size 100×100×50, the defect feature extraction operator... Defined as: ； in, Let p be the temperature gradient magnitude at the vertex p on the triangular mesh surface. Let p be the temperature gradient vector of the mesh vertex on the triangular mesh surface. Let be the second spatial derivative of the thermal field at grid vertex p along spatial direction i. These correspond to the x, y, and z coordinate axes, respectively. The kernels are 3×3×3, corresponding to the x, y, and z directions respectively; Represents a three-dimensional convolution operation. is a rectified linear unit used to introduce nonlinearity while preserving positive response, where p is the index of the mesh vertex on the triangular mesh surface; Through the fully connected layer Projection and calculation of the shrinkage cavity defect probability using the Sigmoid function: ； in, and These are the weight vector and bias scalar of the fully connected layer, respectively. Weight vector Transpose, output Let represent the probability of a shrinkage defect at the vertex p of the triangular mesh surface on the propeller body.

5. The machine learning-based ship propeller design optimization method according to claim 4, characterized in that: Based on the spatial distribution of the probability of shrinkage cavities and hydrodynamic performance, the logic for constructing the optimization objective function is as follows: For the local cross-sectional thickness at the mesh vertex p on the triangular mesh surface Based on its relationship with the critical thickness of thin walls Relationship allocation defects suppress weights : ； in, This is the critical thickness for thin-walled structures. This is the weight growth rate control coefficient, controlling... exist The steep rise in the region; for all conditions that meet the criteria thin-walled regions, Significantly amplify defect penalties; Construct the optimization objective function The calculation formula is as follows: ； in, Let be the set of all mesh vertices in the triangular mesh surface. The total number of grid vertices. To determine the hydrodynamic efficiency based on the current propeller design, Based on the baseline hydrodynamic efficiency, To balance the weights of defect suppression and efficiency preservation; The optimization objective function Minimization using gradient descent aims to simultaneously achieve: 1) targeted suppression of defects in thin-walled regions, i.e., reducing... 2) Relative loss of constrained hydrodynamic efficiency .

6. The machine learning-based ship propeller design optimization method according to claim 5, characterized in that: The logic for backpropagating the gradient of the objective function to the coordinates of the geometric control points is as follows: The geometry of the propeller blades is parameterized by a set of geometric control point coordinates, defined as follows: ,in This represents the three-dimensional coordinates of the e-th geometric control point, where e is the index of the three-dimensional coordinates of the geometric control point. The total number of internal three-dimensional coordinates of the set of geometric control point coordinates; Symbolic distance field It is a set of geometric control point coordinates The scalar field function is determined, and its zero isosurface ... The geometric surface of the propeller is defined; a triangular mesh surface is obtained by discrete sampling based on this zero isosurface, and the coordinates of the geometric control points are established by implicit function theorem regarding the position of the mesh vertex p. Gradient dependency: Optimize the objective function Decomposed into defect prediction items Hydrodynamic performance items Calculate the coordinates of the geometric control points respectively. Gradients and combinations: ； Defect prediction term gradient Calculated using the following chain rule: ； in, The weighted defect penalty coefficient at grid vertex p is... The sensitivity of the thermal-defect characteristic link, For geometric response function, This represents the sensitivity of thickness to heat conduction in the thermodynamic model. Calculate the geometric derivative of the ray projection thickness with respect to the SDF; Gradient of hydrodynamic performance terms Calculated using the differential CFD module: ； Based on gradient The geometric control point coordinates are updated using the gradient descent algorithm. .

7. The machine learning-based ship propeller design optimization method according to claim 6, characterized in that: The logic for iteratively updating the geometric control point coordinate set by repeating steps 1 to 3 is as follows: When the iteration terminates, the final set of geometric control point coordinates is obtained. and based on Reconstructing the symbolic distance field function ,extract The zero isosurface is used to generate a continuously differentiable CAD geometric model through a non-uniform rational B-spline surface fitting algorithm, and the fitting residuals satisfy... The output model format is the industry-standard BREP file; The iteration terminates when any of the following stopping conditions are met, and the final propeller geometry model is output: 1) The average porosity is reduced to below the target level: 2) The relative loss of hydrodynamic efficiency does not exceed the tolerance range, i.e. 3) Optimize the objective function in 5 consecutive iterations The improvement is less than 0.001, and the total number of iterations reaches 200. Before terminating the iteration, a final verification should be performed on the final generated triangular mesh surface, including: verifying the angle between the normal vector at all mesh vertices and the casting direction to ensure the global demolding angle. Verify the conformity of the surface geometry to hydrodynamic performance; generate a propeller geometric model that meets the demolding requirements and takes into account hydrodynamic performance, for use in subsequent detailed design and manufacturing processes.

8. A machine learning-based ship propeller design optimization system, characterized in that: The system is used to execute a machine learning-based ship propeller design optimization method according to any one of claims 1-7, comprising: The surface construction module is used to construct a parametric surface based on the coordinate set of geometric control points of the ship propeller blades, and convert it into an initial triangular mesh surface. It calculates the angle between the normal vector of each vertex of the mesh and the casting direction, identifies vertices with angles less than the preset demolding angle threshold, and adjusts the coordinates of the geometric control points through a gradient optimization algorithm to drive the surface deformation until all vertices meet the demolding angle constraint, and finally generates a triangular mesh surface. The defect calculation module is used to calculate the local cross-sectional thickness of the blade based on SDF. It inputs the triangular mesh surface into the differential thermodynamic model to simulate the evolution of the thermal state field during the casting process. The thermal state field and the local cross-sectional thickness are input into the spatiotemporal feature extraction network to output the spatial distribution of the probability of shrinkage defects in the propeller body. The target optimization module is used to integrate the spatial distribution of the probability of shrinkage defects with hydrodynamic performance, construct the optimization objective function, and propagate the gradient of the optimization objective function from the thermal field through the triangular mesh surface and SDF to the coordinates of each geometric control point through the differential simulation link. Based on the gradient information, the optimization algorithm is used to update the coordinates of all geometric control points synchronously. The iterative update module is used to repeatedly execute steps 1 to 3, iteratively updating the geometric control point coordinate set until the probability of shrinkage defects in the entire domain does not exceed the preset safety threshold, the hydrodynamic performance loss is within the tolerance range, and the optimization objective function converges to a stable range. The loop terminates and outputs the propeller geometric model constructed based on the final geometric control point coordinate set.

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