Method and system for ship propeller design optimization based on machine learning

Abstract

The present application provides a kind of ship propeller design optimization method and system based on machine learning, it is related to ship propeller design technical field, the present application is based on the parameterized surface of geometry control point coordinate set and is converted into symbolic distance field SDF, extracts SDF zero level surface and generates initial grid, satisfies the draft angle constraint by gradient optimization control point, and then calculates the local thickness of blade based on SDF, adopts differentiable thermodynamic model and space-time feature network to predict shrinkage defect probability distribution;Fusion defect probability and hydrodynamic performance construct objective function, through differentiable simulation, the gradient is back propagated to geometry control point by heat field, grid and SDF, drive its synchronous update;Iterative execution above-mentioned process, terminate after meeting defect probability threshold, performance tolerance and convergence condition, output propeller geometry model with excellent hydrodynamic performance and high manufacturability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ship propeller design optimization, in particular to a ship propeller design optimization method and system based on machine learning. BACKGROUND

[0002] As the core component of the ship propulsion system, the geometry design of the ship propeller directly affects the propulsion efficiency, cavitation noise and structural reliability. Modern high-precision propellers usually adopt complex three-dimensional twisted blade modeling to improve the hydrodynamic performance, but such geometry faces serious challenges in the sand casting process. The thin-walled area of the blade is prone to shrinkage defects due to rapid solidification, while the thick area, such as the hub connection, is prone to thermal shrinkage due to uneven heat dissipation. The traditional design process relies on the experience of engineers to repeatedly adjust the blade thickness distribution in CAD software, and then verifies the manufacturability through casting simulation, and finally confirms the performance indicators through water tunnel testing. This process consumes a large amount of computing resources and trial production costs, especially for super large propellers used in liquefied natural gas ships, a single design iteration cycle can last for several months.

[0003] In the prior art, common solutions include using parameterized surfaces combined with CFD / CAE tools for multidisciplinary analysis and optimization, or applying optimization strategies based on experimental design and proxy models to reduce computational cost. Some research also attempts to introduce machine learning methods, such as using neural networks to accelerate flow field prediction or building defect classification models to assist performance and process evaluation. However, these methods still have significant limitations: first, there is a lack of complete differential consistency between geometry representation and simulation modules, which makes the gradient from design variables to objective function unable to be efficiently and accurately back-propagated, and the optimization process relies on discrete iteration and repeated evaluation, which is inefficient; second, existing machine learning assisted methods focus more on performance prediction rather than global coupled optimization, and fail to integrate manufacturing defect prediction and hydrodynamic performance into a unified framework for simultaneous optimization, making it difficult to avoid manufacturability risks in the early design stage.

[0004] In particular, existing methods generally lack an endogenous mechanism for the coordinated optimization of geometry, performance and process. Specifically, in the traditional process, the gradient between geometry modeling and CFD and defect prediction models is broken, and the optimization algorithm cannot respond to the sensitivity of performance targets and defect constraints simultaneously with gradient information, resulting in slow optimization progress and easy falling into local optimum. In addition, process constraints such as draft angle and thickness distribution are often used as post-check conditions rather than embedded optimization targets, causing the design results to still fail to meet casting requirements even after performance meets standards.

[0005] The above information disclosed in the background section is only used to strengthen the understanding of the background of the present disclosure, and therefore it can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0006] The present application aims to provide a ship propeller design optimization method and system based on machine learning to solve the problems raised in the background art.

[0007] To achieve the above-mentioned purpose, the present application provides the following technical solutions:

[0008] A ship propeller design optimization method based on machine learning, the specific steps include:

[0009] Step 1: Construct a parameterized surface according to the geometric control point coordinate set of the ship propeller blade, 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 the vertices with an angle less than a preset demolding angle threshold, adjust the geometric control point coordinates to drive the surface deformation through a gradient optimization algorithm, until all vertices meet the demolding angle constraint, and finally generate a triangular mesh surface;

[0010] Step 2: Calculate the local cross-sectional thickness of the blade based on SDF, input the triangular mesh surface into the differential thermodynamic model, simulate the evolution of the thermal state field during casting, and input the thermal state field and local cross-sectional thickness into the spatiotemporal feature extraction network to output the spatial distribution of propeller body shrinkage defect probability;

[0011] Step 3: Integrate the spatial distribution of shrinkage defect probability and hydrodynamic performance to construct an optimization objective function. Through the differential simulation link, the gradient of the optimization objective function is propagated from the thermal state field to each geometric control point coordinate through the triangular mesh surface and SDF. Based on the gradient information, all geometric control point coordinates are updated simultaneously using an optimization algorithm;

[0012] Step 4: Repeat steps 1 to 3 to iteratively update the geometric control point coordinate set until the global shrinkage defect probability 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.

[0013] Further, the logic for constructing a parameterized surface according to the geometric control point coordinate set of the ship propeller blade is as follows:

[0014] Construct an explicit parameterized surface of the propeller blade based on the geometric control point coordinate set Q, and establish the symbolic distance field corresponding to the parameterized surface , where The zero level surface of is the implicit geometric representation of the parameterized surface;

[0015] Extract the above the initial triangular mesh surface, and the normal vector at each vertex of the initial triangular mesh surface is calculated, which is determined by the gradient direction of the SDF at the vertex;

[0016] point-by-point comparison between the angle between the normal vector at each vertex of the initial triangular mesh surface and the casting direction , identifying all vertices that satisfy , wherein is the demolding angle threshold, which is set according to different regions of the propeller blade: the minimum demolding angle of the pressure surface region of the blade is ; the minimum demolding angle of the suction surface region of the blade is ; the minimum demolding angle of the hub connection region is , and satisfies the constraint condition ;

[0017] for the region where the vertex does not meet the demolding angle threshold: the signed distance field of the parametric surface is represented with the geometric control point coordinate set Q as the independent variable, the demolding angle violation degree of each vertex is calculated, and the sensitivity of the violation degree with respect to the grid vertex is mapped back to Q to obtain the manufacturing constraint gradient, which is transmitted to the geometric control point coordinates via the signed distance field, and the limited numerical optimization of Q is performed based on the manufacturing constraint gradient to drive the local deformation of the parametric surface, the limited numerical optimization is used to ensure the reasonableness of the deformation in the casting direction and suppress the parameter increment that may cause the topological change of the surface, and the iteration is performed until all vertices on the grid satisfy , and the triangular mesh surface that meets the global demolding angle requirement is output.

[0018] Further, based on the SDF, the local cross-sectional thickness of the blade is calculated, and the logic of inputting the triangular mesh surface into the thermodynamic model is:

[0019] Based on the zero-equal surface of the SDF, the local cross-sectional thickness at the grid vertex in the triangular mesh surface is calculated by the ray projection method, and the thickness feature field corresponding to the grid vertex in the triangular mesh surface is generated; the triangular mesh surface is input into the thermodynamic model to simulate the spatio-temporal evolution of the temperature field during the casting process, and the thermal state field is obtained;

[0020] The obtained thermal state field and the corresponding thickness feature field are interpolated and aligned to the same grid resolution, and are input into the spatio-temporal feature extraction network together, to analyze the spatio-temporal evolution law under the thermodynamic-geometric coupling effect, and the spatio-temporal feature extraction network outputs the spatial distribution of the propeller body shrinkage defect probability.

[0021] Further, the logic of outputting the spatial distribution of the propeller body shrinkage defect probability is:

[0022] thermal field After bilinear interpolation resampling and reconstruction into a 3D tensor of size 100×100×50, the defect feature extraction operator... Defined as:

[0023] ;

[0024] 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;

[0025] Through the fully connected layer Projection and calculation of the shrinkage cavity defect probability using the Sigmoid function:

[0026] ;

[0027] 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.

[0028] 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:

[0029] 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 :

[0030] ;

[0031] 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 region, significant amplification of defect penalty;

[0032] constructing the optimization objective function is formulated as follows:

[0033] ;

[0034] where, is the set of all mesh vertices in the triangular mesh surface, is the total number of mesh vertices, is the hydrodynamic efficiency according to the current propeller design, is the baseline hydrodynamic efficiency, is the weight balancing defect suppression and efficiency preservation;

[0035] The optimization objective function is minimized by gradient descent method, aiming to simultaneously achieve: 1) the key suppression of defects in the thin-walled region, i.e., reducing , 2) the relative loss of hydrodynamic efficiency is constrained.

[0036] Further, the logic of back-propagating the gradient of the optimization objective function to the geometry control point coordinates is:

[0037] The geometry shape of the propeller blade is parameterized defined by a set of geometry control point coordinates, defined as where represents the three-dimensional coordinates of the e-th geometry control point, e is the index of the three-dimensional coordinates of the geometry control point, is the total number of three-dimensional coordinates in the set of geometry control point coordinates;

[0038] signed distance field is a scalar field function determined by the set of geometry control point coordinates , whose zero level surface defines the geometric surface of the propeller; based on the zero level surface, a triangular mesh surface is discretely sampled, and the position of the mesh vertex p on the triangular mesh surface establishes a gradient-dependent relationship with the geometry control point coordinates through the implicit function theorem:

[0039] The optimization objective function is decomposed into a defect prediction term and a hydrodynamic performance term , and their gradients with respect to the geometry control point coordinates are calculated and combined:

[0040] ;

[0041] Defect prediction term gradient is calculated by the following chain rule:

[0042] ;

[0043] where, is the weighted defect penalty coefficient at grid vertex p, is the sensitivity of the thermal-defect feature link, is the geometric response function, is the sensitivity of thickness to heat conduction in the thermodynamic model, is the geometric derivative of ray casting thickness calculation on SDF;

[0044] Hydrodynamic performance term gradient is calculated by differentiating the CFD module:

[0045] ;

[0046] Based on the gradient Update the geometric control point coordinates using the gradient descent algorithm .

[0047] Further, the logic of iteratively updating the set of geometric control point coordinates is repeated by performing steps 1 to 3:

[0048] When the iteration is terminated, the final set of geometric control point coordinates is obtained , and the signed distance field function is reconstructed based on , the zero level surface of is extracted, and a continuously differentiable CAD geometric model is generated by a non-uniform rational B-spline surface fitting algorithm, with the fitting residual satisfying , and the output model format is an industrial standard BREP file;

[0049] The iteration is terminated when any of the following stopping conditions is met, and the final propeller geometric model is output:

[0050] 1) The average shrinkage rate is reduced to below the target: , 2) The relative loss of hydrodynamic efficiency does not exceed the tolerance range, i.e. , 3) The improvement amplitude of the comprehensive optimization objective function in the last 5 iterations is less than 0.001, and 4) the total number of iterations reaches 200;

[0051] Before terminating the iteration, a final verification should be performed on the final generated triangular mesh surface, including: rechecking the angle between the normal vector at all grid vertices and the casting direction to ensure that the global demolding angle ​; verify the compliance of the surface geometry with the hydrodynamic performance; generate a propeller geometry model that meets the demolding requirements and takes into account the hydrodynamic performance, for subsequent detailed design and manufacturing processes.

[0052] The application further provides a ship propeller design optimization system based on machine learning, which is used for executing the ship propeller design optimization method based on machine learning.

[0053] A surface construction module is configured to construct a parametric surface according to a set of geometric control point coordinates of a ship propeller blade, convert the parametric surface into an initial triangular mesh surface, calculate the included angle between the normal vector of each vertex of the mesh and the casting direction, identify the vertices with an included angle less than a preset demolding angle threshold, adjust the geometric control point coordinates by using a gradient optimization algorithm to drive the surface deformation, until all the vertices meet the demolding angle constraint, and finally generate a triangular mesh surface.

[0054] A defect calculation module is configured to calculate the local cross-sectional thickness of the blade based on the SDF, input the triangular mesh surface into a differential thermodynamic model, simulate the evolution of the thermal state field in the casting process, and input the thermal state field and the local cross-sectional thickness into a spatiotemporal feature extraction network to output the spatial distribution of the propeller body shrinkage defect probability.

[0055] A target optimization module is configured to comprehensively consider the spatial distribution of the shrinkage defect probability and the hydrodynamic performance, construct an optimization target function, and through a differential simulation link, propagate the gradient of the optimization target function from the thermal state field to each geometric control point coordinate through the triangular mesh surface and the SDF, and based on the gradient information, synchronously update all the geometric control point coordinates by using an optimization algorithm.

[0056] An iterative update module is configured to repeatedly execute steps 1 to 3 to iteratively update the set of geometric control point coordinates until the shrinkage defect probability in the whole domain is less than a preset safety threshold, the loss of the hydrodynamic performance is within a tolerance range, and the optimization target function converges to a stable range, terminate the cycle, and output a propeller geometry model constructed based on the final set of geometric control point coordinates.

[0057] Compared with the prior art, the application has the following beneficial effects:

[0058] The application introduces the demolding angle constraint in the early optimization stage, dynamically adjusts the control point coordinates by using the gradient algorithm, and drives the surface morphology to change, so as to fundamentally avoid the process defects caused by insufficient demolding angle in the early design stage, and overcomes the lag and passivity caused by the post-check of the manufacturing constraint in the traditional method.

[0059] 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.

[0060] 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

[0061] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0062] Figure 2 This is a line graph of the defect suppression weight-optimization objective function of this invention;

[0063] Figure 3 This is a kite diagram of the defect suppression weight, shrinkage defect probability, and optimization objective function of this invention.

[0064] Figure 4 The objective function for this invention is the current hydrodynamic probability bubble diagram.

[0065] Figure 5 This is a curve showing the fitting of the defect suppression weights and the optimization objective function in this invention.

[0066] Figure 6 This is a flowchart of the overall system modules of the present invention. Detailed Implementation

[0067] 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.

[0068] It should be noted that unless otherwise defined, technical terms or scientific terms used in the present application shall have the common meaning understood by one of ordinary skill in the art to which the present application pertains. The terms "first", "second", and similar terms used in the present application do not denote any order, number, or importance, but are used to distinguish different components. The terms "include", "contain", and similar terms mean that the elements or objects before the terms encompass the elements or objects listed after the terms and their equivalents, and do not exclude other elements or objects. The terms "connected" or "connected" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right", and the like are used only to indicate relative positional relationships, which may change accordingly when the absolute position of the described object changes.

[0069] Embodiments:

[0070] Referring to Figures 1-5 , the present application provides a technical solution:

[0071] A ship propeller design optimization method based on machine learning, the specific steps comprising:

[0072] Step 1: Construct a parameterized surface according to the geometric control point coordinate set of the ship propeller blade, 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 the vertices with an angle less than a preset demolding angle threshold, adjust the geometric control point coordinates to drive the surface deformation through a gradient optimization algorithm, until all vertices meet the demolding angle constraint, and finally generate a triangular mesh surface;

[0073] The logic for constructing a parameterized surface according to the geometric control point coordinate set of the ship propeller blade is:

[0074] Based on the geometric control point coordinate set Q, an explicit parameterized surface of the propeller blade is constructed, and a symbolic distance field corresponding to the parameterized surface is established , wherein The zero level surface of is the implicit geometric representation of the parameterized surface;

[0075] These geometric control point coordinates are connected, interpolated, and smoothly spread into a complete surface through mathematical methods such as NURBS, B-spline, etc., and an explicit parameterized surface is obtained. Its explicitness is that the points on the surface can be directly expressed by a parameter equation; its parameterization means that by adjusting the positions of the control points in Q, the entire surface shape can be directly and intuitively driven to change;

[0076] SDF converts the explicit surface into an implicit scalar field, and any point The value of the point to the propeller surface represents the shortest distance, and the point is agreed to be negative when inside the object and positive when outside, the SDF is equal to zero, that is, the zero surface, which accurately restores the original propeller surface. The advantage of this implicit expression is that it naturally avoids the self-intersection and crack problems that may occur in explicit representation, and is very convenient for topology change and Boolean operation;

[0077] The zero surface of the above is converted into an initial triangular mesh surface by an isosurface extraction algorithm, and the normal vector at each vertex of the initial triangular mesh surface is calculated, which is determined by the gradient direction of the SDF at the vertex; The casting direction refers to the relative motion direction of the mold when the molten metal is injected into the mold and solidified into a propeller blade, and then the mold is opened and the casting is taken out, Emphasize that SDF is uniquely determined by the control point set Q;

[0078] The initial triangular mesh surface is generated from the zero surface of SDF by an isosurface extraction algorithm such as the classic Marching Cubes or its improved algorithm, which is the key link to discretize the continuous mathematical expression into a face model that can be directly processed and displayed by the computer. The calculation of the normal vector at each vertex of the grid is the basis for subsequent judgment of the demolding angle, which makes use of a unique feature of SDF: the gradient vector direction at any point is the normal direction of the isosurface at that point, and is a unit vector;

[0079] The casting direction is a core concept derived from the actual production process, which defines the direction of moving the mold or the casting to take it out after solidification in the mold. Any surface parallel to this direction or with a small included angle will cause serious friction and scratching with the mold during demolding, resulting in the part being unable to be taken out or the surface quality being damaged, so it is necessary to calculate the included angle between the normal vector at each vertex of the grid and the fixed casting direction;

[0080] Point-by-point comparison of the included angle between the normal vector at each vertex of the initial triangular mesh surface and the casting direction Identify all vertex regions that satisfy , where is the demolding angle threshold, and the minimum demolding angle is set according to different regions of the propeller blade: the minimum demolding angle of the pressure surface region of the blade is ; the minimum demolding angle of the suction surface region of the blade is ; the minimum demolding angle of the hub connection region is , and satisfies the constraint condition ;

[0081] The normal vector is the core geometric quantity to judge the draft angle. For discrete triangular mesh, the normal vector is usually calculated by averaging the normals of adjacent faces. This method is prone to errors on low-quality meshes. The method uses a key mathematical property of SDF: the gradient vector of SDF at a point is the normal of the iso-surface 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, which is not affected by mesh quality;

[0082] The hub connection area usually has complex structure, large thickness variation and the largest demolding resistance, so the most stringent maximum draft angle threshold is given The pressure surface of the blade is the main working surface to push the water flow, so its geometric fidelity is required to be high, but the demolding difficulty is moderate, and the threshold is relatively loose, while the process constraint of the suction surface is usually the lowest, so the threshold is the most relaxed;

[0083] For the region where the included angle does not reach the threshold of the draft angle: the signed distance field of the parameterized surface is represented by the geometric control point coordinate set Q as the independent variable , the draft angle violation degree of each vertex is calculated, and the sensitivity of the violation degree to the mesh vertex is transmitted back to Q along the mapping to obtain the manufacturing constraint gradient, which is transmitted to the geometric control point coordinates via the signed distance field. Based on the manufacturing constraint gradient, the Q is updated by limited numerical optimization to drive the local deformation of the parameterized surface, and the limited numerical optimization is used to ensure the rationality of the deformation in the casting direction and to suppress the parameter increment that may cause the topological change of the surface. Iterate until all vertices on the mesh satisfy , and output the triangular mesh surface that meets the global draft angle requirement;

[0084] The requirement of this qualitative problem is converted into a quantifiable mathematical objective, and the violation degree can be simply defined as This function means that if the included angle has met the requirement, i.e. greater than or equal to , the violation degree is 0 and no punishment is needed; if it does not meet the requirement, the violation degree is positive, and the greater the gap, the higher the violation degree. This function provides a clear objective for optimization: to minimize the total violation degree of all vertices;

[0085] Sensitivity refers to how sensitive the vertex's violation degree change is to the geometry change of the vertex itself, and mapping refers to a set of calculation chains from the geometry control point coordinates to the SDF to the mesh vertex p to the normal vector to the included angle to the violation degree. Through the chain rule, the algorithm can automatically and accurately deduce from the sensitivity of the vertex violation degree how each geometry control point coordinate should be moved and how much it should be moved to most effectively reduce the total violation degree. This deduced direction is to create a constraint gradient, which is equivalent to the computer automatically performing a perfect sensitivity analysis and finding the optimal modification path.

[0086] Fine-tune the geometry control point coordinates according to the gradient calculated in the previous step. This is an iterative process: fine-tune a little geometry control point coordinate each time → update SDF and mesh vertex → recalculate violation degree and gradient → fine-tune again; Restriction and local deformation are key. Optimization is not a wild and crazy ride, but a controlled and fine one. It only moves those control points that are most effective in solving the demolding problem, so that deformation mainly occurs near the problem area, maximizing the preservation of the original design shape of the other parts of the propeller;

[0087] The meaning of "the restricted numerical optimization is used to ensure the reasonableness of the deformation in the casting direction and to suppress the parameter increment that may cause changes in the topology of the curved surface" is to ensure the reasonableness of the deformation in the casting direction, which means that the optimization will preferentially guide the curved surface to expand or adjust in a 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 the object, such as the number of blades and whether there are holes on the blades. This rule prohibits the optimization process from changing the topology structure, such as it does not allow two blades to fuse together or a closed curved surface to tear a hole in order to increase the demolding angle. It ensures that the final result is still a usable propeller;

[0088] The above process is run in a loop until it is detected that each point fully meets the demolding angle requirement of the area it is in. The final output is no longer just a design model, but a design-as-manufactured product model that has passed manufacturability certification.

[0089] Step 2: Calculate the local section thickness of the blade based on SDF, input the triangular mesh surface into the differential thermodynamic model, simulate the evolution of the thermal state field during casting, and input the thermal state field and local section thickness into the space-time feature extraction network to output the spatial distribution of the propeller body shrinkage defect probability;

[0090] The logic for calculating the local section thickness of the blade based on SDF and inputting the triangular mesh surface into the differential thermodynamic model is as follows:

[0091] Based on the zero level surface of SDF, the ray casting method is used to calculate the local section thickness of the grid vertices in the triangular mesh surface, and the thickness feature field corresponding to the grid vertices in the triangular mesh surface is generated; the triangular mesh surface is input into the sub-thermodynamic model to simulate the space-time evolution of the temperature field in the casting process, and the thermal state field is obtained;

[0092] At each vertex p of the grid, a ray is emitted along its normal direction (both positive and negative directions), which will intersect with the zero level surface of SDF (i.e. the other side surface of the propeller), the distance between the grid vertex p and the intersection point is calculated, which is the local section thickness at that point, and a thickness feature field covering the entire propeller surface is formed by calculating the thickness value for each grid vertex;

[0093] The geometric model of the propeller (triangular mesh defines the boundary of the calculation domain) is input into a simplified computational fluid dynamics / heat transfer model, which solves the heat conduction equation to simulate the temperature change of each point inside the propeller at different times from pouring to complete solidification, and the thermal state field records the temperature history of each grid vertex p at each time;

[0094] The obtained thermal state field and the corresponding thickness feature field are interpolated and aligned to the same grid resolution, and are input into the space-time feature extraction network to analyze the space-time evolution law under the thermodynamic-geometric coupling effect, and the space-time feature extraction network outputs the spatial distribution of the propeller body shrinkage cavity defect probability;

[0095] Standardized input data are prepared for the neural network, the thermal field (from the volume grid) and the thickness field (from the surface grid) usually have different spatial resolutions and data formats, through interpolation techniques such as bilinear interpolation, the thermal state field and the thickness field are resampled to the same regular three-dimensional grid, i.e. 100x100x50 grid, to ensure that each grid element has temperature and thickness values, and the defect is the result of thermal-geometric coupling, only the temperature field cannot know whether it is thick or thin at this place, only the thickness field cannot know how fast it cools at this place, both must be combined, and the network can learn the complex rule that defects are prone to occur in thick and slow cooling places;

[0096] 100x100x50 is to divide the physical space into 100x100x50 cubic / rectangular voxels, which is a three-dimensional grid size, 100 (x direction) means that the physical domain is equally divided into 100 units in 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;

[0097] 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. ;

[0098] The logic for outputting the spatial distribution of the probability of shrinkage defects in the propeller body is as follows:

[0099] thermal field After bilinear interpolation resampling and reconstruction into a 3D tensor of size 100×100×50, the defect feature extraction operator... Defined as:

[0100] ;

[0101] 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;

[0102] 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.

[0103] 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.

[0104] reflects the coupling effect of cooling rate and hot spot intensity, which indicates the severity of a place being both a hot spot and having a slow cooling rate, if a point is a strong hot spot ( for a large positive value), but cools very fast ( very small), the product will be a large positive value, which perfectly indicates the most dangerous defect region, this product term is the key physical feature for defect identification; for a large positive value), and cools very slowly ( very small), the product will be a large positive value, which perfectly indicates the most dangerous defect region, this product term is the key physical feature for defect identification;

[0105] three different direction convolution kernels are used to process the hot spot features in three directions respectively, then summed up, in order 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 that are judged to be potentially dangerous (i.e. the product term is positive) will be retained and passed to the next layer, negative values such as features of regions that cool quickly or are not hot spots are suppressed to 0, which introduces nonlinearity and lets the network focus on the "bad" signal;

[0106] In summary, is a high-dimensional feature vector, the size of the value in each dimension of which reflects the possibility of the grid vertex p and its neighborhood being a dangerous hot spot, the larger the value, the higher the risk of defect characteristics of the region;

[0107] Through the fully connected layer, is projected and the probability of shrinkage hole defects is calculated by the Sigmoid function:

[0108] ;

[0109] where, and are the weight vector and bias scalar of the fully connected layer respectively, is the transpose of the weight vector , and the output represents the probability of shrinkage hole defects of the propeller body at the grid vertex p on the triangular mesh surface;

[0110] This formula maps the complex physical features extracted in the last step to a simple scalar with a clear probability meaning, the role of the Sigmoid function is to compress a real number in an arbitrary range to , which meets the definition of probability; reflects all defect features the weighted integrated score, the weight is trained by the network, which determines the importance of different features to the final decision; the higher the integrated score, the more support the "this point has defects" judgment is gathered by all features;

[0111] Sigmoid function output reflects the defect probability calculated based on the integrated score, for example indicates that the model predicts that there is a 95% probability of shrinkage at this point; the greater the value → the output of the sigmoid function is closer to 1 → the defect probability is higher, the smaller (more negative) the value → the output of the sigmoid function is closer to 0 → the defect probability is lower.

[0112] Step 3: Integrate the spatial distribution of shrinkage defect probability and hydrodynamic performance to construct the optimization objective function, and through the differential simulation link, the gradient of the optimization objective function is propagated from the thermal state field to each geometric control point coordinate through the triangular mesh surface, SDF. Based on the gradient information, all geometric control point coordinates are updated synchronously using the optimization algorithm;

[0113] The logic of constructing the optimization objective function by integrating the spatial distribution of shrinkage defect probability and hydrodynamic performance is:

[0114] For the local section thickness at the grid vertex p on the triangular mesh surface , based on the relationship between the critical thickness of the thin-walled , the defect suppression weight is distributed:

[0115] ;

[0116] wherein, is the critical thickness of the thin-walled, is the weight growth rate control coefficient, which controls the steep rise amplitude in the region; for all thin-walled regions that satisfy , significantly amplifies the defect penalty;

[0117] reflects the degree to which the grid vertex p needs to be paid special attention due to insufficient thickness, which indicates the severity and sensitivity of the defect risk at this point, the greater, the thinner the region where the point is located (the is much smaller than ), the higher the urgency and importance of reducing the defect probability at this point in the optimization process.

[0118] 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.

[0119] 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.

[0120] Construct the optimization objective function The calculation formula is as follows:

[0121] ;

[0122] 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;

[0123] 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.

[0124] 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 aggressive the optimization algorithm will reduce the defect risk, even at the expense of certain efficiency loss; is the current, dynamic performance indicator, which is the tuning object of the optimization process, is the fixed, static reference value, which is the yardstick to measure the performance change;

[0125] represents the triangular mesh surface generated based on the current iteration of the geometric control point coordinate set Q, and the hydrodynamic efficiency value calculated by the hydrodynamic performance evaluation model. In each optimization iteration, the process is as follows: define the geometric shape from the current geometric control point coordinate set Q, generate the corresponding triangular mesh surface through the geometric shape; input this triangular mesh surface into a verified hydrodynamic performance evaluation module, which can be: a high-fidelity computational fluid dynamics solver, which calculates the efficiency by numerically simulating the thrust and torque of the propeller at a certain speed ; is a variable, whose value changes dynamically with the updating of the geometric control point coordinate set Q and the change of the geometric shape, and it is the output feedback of the optimization process;

[0126] is a fixed reference value, representing the hydrodynamic efficiency of the initial design or a certain recognized design state, and the reference hydrodynamic efficiency is set to 0.75, which is the hydrodynamic efficiency evaluation value of the initial propeller design model, and its main function is to normalize the efficiency loss term , which makes this loss term become a dimensionless relative value, easy to understand, and matches the defect term (also a scalar around 0 to 1) in numerical scale, so as to effectively balance the weighting factor between the two competing objectives. Without this normalization, it will need to make huge adjustments according to the absolute numerical range of , which is very inconvenient;

[0127] The optimization objective function is minimized by gradient descent method, aiming to simultaneously achieve: 1) focus on suppressing defects in thin-walled areas, i.e. reducing , 2) constrain the relative loss of hydrodynamic efficiency ;

[0128] Some data numbers and specific data of the optimization objective function are shown in Table 1.

[0129] Table 1

[0130]

[0131] Through the analysis of the data, it is observed that there is a certain correlation between different characteristic parameters. For example, from the data, it can be seen that the synergistic effect of defect suppression weight and shrinkage defect probability has a significant impact on the optimization objective function value. When both the defect suppression weight and the shrinkage defect probability are at a high level, such as in sample No. 6, the defect suppression weight is 0.9 and the shrinkage defect probability is 0.6, the optimization objective function value reaches 0.480. In sample No. 7, although the shrinkage defect probability reaches 0.7, the optimization objective function value is relatively low, which is 0.093, because the defect suppression weight is only 0.1. This shows that in the manufacturing process, implementing key suppression on high defect risk areas can effectively improve the overall quality performance.

[0132] In the analysis of the relationship between hydrodynamic efficiency and optimization objective function value, with the improvement of hydrodynamic efficiency, the optimization objective function value shows a gradually decreasing trend. For example, in sample No. 3, the hydrodynamic efficiency is 0.76, and the corresponding optimization objective function value is 0.307. In sample No. 9, the hydrodynamic efficiency decreases to 0.70, and the optimization objective function value increases significantly to 0.627. This shows that higher propeller efficiency helps to reduce the overall optimization objective function value, but it needs to be noted that when the surface quality risk is high, even if the hydrodynamic efficiency is good, the optimization objective function value may still be at a high level.

[0133] Further observation shows that when the surface quality risk indicator, i.e. the product of the defect suppression weight and the shrinkage defect probability, is maintained at a low level, even if the hydrodynamic efficiency is mediocre, the optimization objective function value can still be kept within a reasonable range. For example, in sample No. 1, the surface quality risk is low, the hydrodynamic efficiency is 0.72, and the optimization objective function value is only 0.063. This shows that in the design process of the propeller, the balance between surface quality characteristics and fluid dynamic performance needs to be considered. By optimizing the distribution of geometric feature control points, the overall goal of controlling defect risk while ensuring hydrodynamic efficiency can be achieved.

[0134] The logic of propagating the gradient of the optimization objective function to the geometric control point coordinates is as follows:

[0135] The geometric shape of the propeller blade is defined by a set of geometric control point coordinate parameters. The geometric control point coordinate set is defined as where represents the three-dimensional coordinates of the e-th geometric control point, e is the index of the three-dimensional coordinates of the geometric control point, is the total number of three-dimensional coordinates in the geometric control point coordinate set;

[0136] Symbolic distance field is a scalar field function determined by the geometric control point coordinate set , whose zero level surface 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:

[0137] Optimize the objective function Decomposed into defect prediction items Hydrodynamic performance items Calculate the coordinates of the geometric control points respectively. Gradients and combinations:

[0138] ;

[0139] 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;

[0140] Defect prediction term gradient Calculated using the following chain rule:

[0141] ;

[0142] 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;

[0143] 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;

[0144] is the sensitivity of the thermal state field to local thickness, which is the core output of the differentiable thermodynamic model, and it precisely answers the question “if this point becomes a little bit thicker (or thinner), how will it affect its cooling process”, thickness increase usually leads to slower cooling , and more likely to form thermal nodes;

[0145] This link answers the question “moving the geometry control point coordinates , how will it change the thickness at mesh vertex p”, it contains two paths: 1) shape change leads to direct thickness change, control point moving → SDF changing → ray penetration path changing → thickness changing; 2) vertex moving leads to indirect thickness change, control point moving → mesh vertex p’s position slightly moving → re-evaluating thickness at the new position;

[0146] Each intermediate sensitivity in the gradient propagation link, including but not limited to , etc, its calculation relies on integrating geometry modeling, physics simulation, defect prediction, etc. modules into a differentiable programming framework, thus forming an end-to-end differentiable computation graph, in which the above sensitivities are automatically calculated by the automatic differentiation function of the framework during backpropagation, specifically by implementing the differentiable thermodynamic model, it ensures the differentiability of the temperature field to local thickness ; by implementing the differentiable ray casting algorithm, it ensures the differentiability of local thickness to signed distance field ;

[0147] hydrodynamic performance term gradient is calculated by differentiating the CFD module:

[0148] ;

[0149] represents the current hydrodynamic efficiency sensitivity to each control point moving, it calculates “if I push this control point a little bit in a certain direction, how much will the propeller’s efficiency change”, this gradient field is usually very complex, containing all the information of fluid and complex geometry interaction; the negative sign is to maximize the efficiency , but the optimization goal is to minimize , hydrodynamic efficiency increase will lead to decrease, thus making reduce, so the direction of the gradient is the direction to improve efficiency, directly used in the gradient descent update of the reduced

[0150] The implementation of the differentiable thermodynamic model is based on a computational framework with automatic differentiation function. In the implementation, the computational domain is discretized into grids, and the temperature of each grid cell is taken as a variable. The heat flow calculation based on Fourier's law, time integration step, and other numerical solution operations are all implemented as differentiable operations (such as tensor operations) under the framework. Thus, the entire process from input (such as boundary geometry, material properties) to output (temperature field) constitutes a differentiable computation graph, and the framework can automatically calculate the gradient of the output with respect to the input, i.e., obtain the sensitivity, etc. Based on the gradient The gradient descent algorithm is used to update the coordinates of the geometric control points , and the specific steps include:

[0151] Let the overall gradient vector be:

[0152] ;

[0153] where, is the transpose symbol; this is a global overview of the optimization direction for all control points, which concatenates the gradients of all control points (each is a three-dimensional vector) into a very long column vector The dimension of this vector is 3n x 1 (n points, each with x, y, z three coordinate directions). In order to perform subsequent global gradient clipping, the optimization process needs to consider the update pace of all control points at the same time to avoid the update amplitude of some points being too large and damaging the overall optimization stability. Calculating the norm of this overall vector is to measure the size of the total gradient in the current optimization step;

[0154] The gradient descent algorithm with momentum is used to update the coordinates of the geometric control points:

[0155] This indicates that the most basic gradient descent method is not used, but two advanced optimization techniques, momentum + gradient clipping, are used to accelerate convergence and improve stability. This is the core idea of modern deep learning optimizers, such as Adam and RMSProp, which include these ideas.

[0156] ;

[0157] where, is the learning rate, is the momentum coefficient, is the gradient clipping threshold, is the iteration number, 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.

[0158] 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.

[0159] 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.

[0160] 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;

[0161] 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.

[0162] 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.

[0163] Step 4: Repeat steps 1 to 3 to iteratively update the set of geometric control point coordinates until the shrinkage defect probability of 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 set of geometric control point coordinates;

[0164] Repeat steps 1 to 3 to iteratively update the set of geometric control point coordinates:

[0165] When the iteration is terminated, the final set of geometric control point coordinates is obtained , and based on the signed distance field function is reconstructed , the zero iso-surface of is extracted, and a continuous and differentiable CAD geometric model is generated through a non-uniform rational B-spline surface fitting algorithm, the fitting residual satisfies , and the model format is an industrial standard BREP file;

[0166] The optimization process internally 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 reconstructs smooth and parameterized surfaces from discrete grid points. Such surfaces are continuous and differentiable, meaning they have no sharp points or corners, which is crucial for fluid dynamics performance and numerical control machining;

[0167] This requirement ensures that the fitted NURBS surface is highly consistent with the SDF zero iso-surface (i.e. the ideal design shape) obtained from optimization, with minimal residual error, indicating that the CAD model perfectly reproduces the results of the optimization design without introducing shape errors;

[0168] BREP (Boundary Representation) is the mainstream format for describing solid models and can be read by all CAD software such as CATIA, SolidWorks, NX, and CAE / CAM software. Outputting a BREP file means that the optimization design results can be directly used for: adding machining allowances, labels, etc., designing mold cores and cavities based on this model, generating G code for driving numerical control machine tools, and performing more detailed finite element analysis;

[0169] The iteration is terminated when any of the following stopping conditions are met, and the final propeller geometric model is output:

[0170] 1) The average shrinkage rate decreases below the target: , which reflects the average defect risk level of the whole propeller surface, it averages the predicted probability at all vertices to get a macroscopic quality indicator, which indicates the overall casting quality of this design scheme; the larger the value is, the higher the overall possibility of shrinkage defects in the whole casting is, and the worse the average quality is; less than 0.005 is a very strict quality target, which means that on average only 5 points out of 1000 are considered to be at risk of defects, which is equivalent to setting a high standard that more than 99.5% of the area is safe;

[0171] 2) The relative loss of hydrodynamic efficiency is not more than the tolerance range, that is, , which reflects the percentage change of the hydrodynamic performance of the current design scheme relative to the performance of the benchmark design, which indicates the performance cost paid for improving manufacturability; the larger the value is, the greater the performance loss is, and a value of 0.01 means that the efficiency is reduced by 1%, the current efficiency is lower, , the smaller the ratio of , the greater the difference is, and the greater the relative loss of performance is; less than 0.005 is a performance protection tolerance, which limits the performance loss to within 0.5%, which means that the efficiency of the optimized design cannot be lower than 99.5% of the benchmark efficiency, this condition ensures that the optimization process will not excessively sacrifice the core function of the propeller - propulsion efficiency in pursuit of extreme manufacturability;

[0172] 3) The improvement of the comprehensive optimization objective function is less than 0.001 in 5 consecutive iterations, and 4) the total number of iterations reaches 200, which reflects the convergence state of the optimization process, when consecutive iterations cannot significantly reduce the value of the objective function, it means that the algorithm has found a (possibly local) optimal solution, which indicates that the optimization process has "squeezed" all the potential under the current design framework, and there is little benefit to continue iterating; less than 0.001 is a convergence precision indicator. It requires that the value of the optimization objective function in 5 consecutive iterations is very small (less than 0.001) each time, which indicates that the optimization process has stabilized; "5 consecutive iterations" is a robust design to prevent premature termination, a single iteration improvement is small, which may be random fluctuations, and 5 consecutive small iterations strongly indicate that convergence has occurred;

[0173] Before terminating the iteration, the final generated triangular mesh surface should be subjected to final verification, including: rechecking the angle between the normal vector at all mesh vertices and the casting direction to ensure that the global draft angle ; verify the compliance of the surface geometry with the hydrodynamic performance;

[0174] Generate a propeller geometry model that meets the demolding requirements and takes into account the hydrodynamic performance for subsequent detailed design and manufacturing processes.

[0175] Referring to Figure 6 The application further provides a ship propeller design optimization system based on machine learning, which is used to execute the above-mentioned ship propeller design optimization method based on machine learning, and comprises:

[0176] A curved surface construction module is configured to construct a parametric curved surface according to a set of geometric control point coordinates of a propeller blade, convert the parametric curved surface into an initial triangular mesh curved surface, calculate an included angle between a normal vector of each vertex of the mesh and a casting direction, identify a vertex with an included angle less than a preset demolding angle threshold, adjust the geometric control point coordinates by using a gradient optimization algorithm to drive the curved surface to deform until all the vertices satisfy the demolding angle constraint, and finally generate a triangular mesh curved surface.

[0177] A defect calculation module is configured to calculate a local cross-sectional thickness of the blade based on the SDF, input the triangular mesh curved surface into a differential thermodynamic model, simulate evolution of a thermal state field in a casting process, and input the thermal state field and the local cross-sectional thickness into a spatiotemporal feature extraction network together to output a spatial distribution of propeller body shrinkage defect probability.

[0178] A target optimization module is configured to comprehensively consider the spatial distribution of the shrinkage defect probability and the hydrodynamic performance, construct an optimization target function, propagate a gradient of the optimization target function from the thermal state field to each geometric control point coordinate through the triangular mesh curved surface and the SDF in a reverse direction by using a differential simulation link, and synchronously update all the geometric control point coordinates based on the gradient information by using an optimization algorithm.

[0179] An iterative updating module is configured to repeatedly execute steps 1 to 3 to iteratively update the set of geometric control point coordinates until the shrinkage defect probability in the whole domain is less than a preset safety threshold, the loss of the hydrodynamic performance is within a tolerance range, and the optimization target function converges to a stable range, terminate the loop, and output a propeller geometric model constructed based on the final set of geometric control point coordinates.

[0180] The above formulas are all dimensionless numerical calculations, and the formulas are obtained by collecting a large amount of data to simulate a formula closest to the actual situation. The preset parameters in the formula are set by a person skilled in the art according to the actual situation.

[0181] The above embodiments can be realized wholly or partially by software, hardware, firmware or any combination thereof. When realized by software, the above embodiments can be realized in the form of a computer program product wholly or partially. A person skilled in the art can realize that the units and algorithm steps of the examples described in connection with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized by hardware or software methods depends on the specific application and design constraints of the technical solutions.

[0182] The units described as separate components may or may not be physically separate, and the components displayed as units may or may not be physical units, and may be located in one place, or distributed on multiple network units. Part or all of the units can be selected to achieve the purpose of the embodiment of the present application according to actual needs.

[0183] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A machine learning based method for ship propeller design optimization, characterized in that, The specific steps include: Step 1: Construct a parametric surface according to the geometric control point coordinate set of the ship propeller blade, 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 the vertices with an angle smaller than a preset demolding angle threshold. Adjust the geometric control point coordinates through a gradient optimization algorithm to drive the surface deformation until all vertices meet the demolding angle constraint. 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 casting. Input the thermal state field and local cross-sectional thickness into the spatiotemporal feature extraction network to output the spatial distribution of propeller body shrinkage defect probability; Step 3: Integrate the spatial distribution of shrinkage defect probability and hydrodynamic performance to construct an optimization objective function. Through the differential simulation link, the gradient of the optimization objective function is propagated from the thermal state field to each geometric control point coordinate through the triangular mesh surface and SDF. Based on the gradient information, update all geometric control point coordinates simultaneously using an optimization algorithm; Step 4: Repeat steps 1 to 3 to iteratively update the geometric control point coordinate set until the global shrinkage defect probability 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 calculating the local cross-sectional thickness of the blade based on SDF is as follows: Based on the zero-level surface of SDF, the local cross-sectional thickness at the grid vertices in the triangular mesh surface is calculated using the ray projection method to generate a thickness feature field corresponding to the grid vertices in the triangular mesh surface. Input the triangular mesh surface into the differential thermodynamic model to simulate the spatiotemporal evolution of the temperature field during casting and obtain the thermal state field; Interpolate and align the obtained thermal state field and the corresponding thickness feature field to the same grid resolution, and input them 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 propeller body shrinkage defect probability; The logic for outputting the spatial distribution of propeller body shrinkage defect probability is as follows: Resample the thermal state field T(p) by bilinear interpolation and reconstruct it into a three-dimensional tensor with dimensions 100x100x50. The defect feature extraction operator F(p) is defined as: wherein, is the magnitude of the temperature gradient at a grid vertex p on the triangular mesh surface, is the temperature gradient vector at a grid vertex p on the triangular mesh surface, is the second-order spatial derivative of the thermal state field at a grid vertex p along a spatial direction i, i = 1, 2, 3 corresponding to the x, y, z coordinate axis directions, K i is a 3x3x3 convolution kernel corresponding to the x, y, z directions, respectively; * denotes a three-dimensional convolution operation, ReLU is a rectified linear unit used to introduce nonlinearity and preserve positive responses, and p is the index of a grid vertex on the triangular mesh surface. Project F(p) through a fully connected layer and calculate the shrinkage defect probability through the Sigmoid function: where W and b are the weight vector and bias scalar of the fully connected layer, respectively, W T is the transpose of the weight vector W, and the output D(p) ∈ [0, 1] represents the shrinkage defect probability of the propeller body at the mesh vertex p on the triangular mesh surface.

2. The method of claim 1, wherein: The logic for constructing a parametric surface based on the geometric control point coordinate set of the ship propeller blade is as follows: Based on the geometric control point coordinate set Q, construct an explicit parametric surface of the propeller blade. Establish the corresponding signed distance field SDF(x; Q) of the parametric surface, where the zero-level surface of SDF(x; Q) is the implicit geometric representation of the parametric surface; The zero level surface of the SDF(x;Q) is converted into an initial triangular mesh surface by an isosurface extraction algorithm, and the normal vector at each vertex of the initial triangular mesh surface is calculated, which is determined by the gradient direction of the SDF at the vertex; Point-by-point comparison of the angle θ between the normal vector of each vertex on the initial triangular mesh surface and the casting direction, identify all vertices that satisfy θ < θ min , wherein θ min is the demolding angle threshold, according to different regions of the propeller blade, the minimum demolding angle of the pressure surface region of the blade is T p , the minimum demolding angle of the suction surface region of the blade is T s , the minimum demolding angle of the hub connecting region is T h , and the constraint condition T h >T p >T s is satisfied; For the region where the vertex angle is less than the threshold of the draft angle, a signed distance field SDF(x; Q) is used to represent the parameterized surface with the set of geometric control point coordinates Q as the independent variable. The draft angle violation degree of each vertex is calculated, and the sensitivity of the violation degree with respect to the grid vertex is transmitted back to Q along the mapping to obtain the manufacturing constraint gradient, which is transmitted to the geometric control point coordinates via the signed distance field. Based on the manufacturing constraint gradient, a limited numerical optimization is performed on Q to drive the local deformation of the parameterized surface. The limited numerical optimization is used to ensure the reasonableness of the deformation in the casting direction and to suppress the parameter increment that may cause the topological change of the surface. The iteration is performed until all the vertices on the grid satisfy θ≥θ min , and the triangular mesh surface that meets the global draft angle requirement is output.

3. The method of claim 2, wherein: The logic for constructing the optimization objective function J is as follows: For the local section thickness τ(p) at a mesh vertex p on a triangular mesh surface, a defect suppression weight w(p) is assigned based on its relation to a thin-walled critical thickness τ min ​ Where, τ min =2 represents the critical thickness of the thin-walled structure, and α is the weighted growth rate control coefficient, which controls w(p) to be within τ(p) < τ. min The steep rise in the region; for all regions satisfying τ(p) < τ min In thin-walled regions, w(p) significantly amplifies the defect penalty; The calculation formula of the optimization objective function J is as follows: Wherein, P is the set of all grid vertices in the triangular mesh surface, |P| is the total number of grid vertices, η is the hydrodynamic efficiency according to the current propeller design, η0 is the baseline hydrodynamic efficiency, and λ>0 is the weight balance between defect suppression and efficiency maintenance. The optimization objective function J is minimized by a gradient descent method aiming at simultaneously achieving: 1) a focus on the inhibition of defects in thin-walled areas, i.e. reducing w(p) x D(p), 2) a relative loss of constraint on the hydrodynamic efficiency 4. The method of claim 3, wherein: The logic for propagating the gradient of the optimization objective function to the coordinates of the geometric control points is as follows: The geometry of the propeller blade is parameterized by a set of geometry control point coordinate sets, defined as Q = {q1, q2,..., q e ,…,q n} where represents the three-dimensional coordinates of the e-th geometry control point, e is the index of the three-dimensional coordinates of the geometry control point, and n is the total number of three-dimensional coordinates of the geometry control point coordinate set. The symbol distance field SDF(x; Q) is a scalar field function determined by the set of geometric control point coordinates Q, and the zero-equal surface SDF(x; Q)=0 defines the geometric surface of the propeller; based on the zero-equal surface, a triangular mesh surface is obtained by discrete sampling, and the position of the mesh vertex p on the triangular mesh surface is established through the gradient dependence relationship of the implicit function theorem on the geometric control point coordinates q e . The optimization objective function J is decomposed into a defect prediction term and a hydrodynamic performance term The gradients of each with respect to the geometry control point coordinates q e are calculated separately and combined: Defect prediction term gradient is calculated by the following chain rule: where A(p) = w(p) / |P| is the weighted defect penalty coefficient at grid vertex p, is the sensitivity of the thermal-defect feature link, is the geometric response function, is the sensitivity of the thickness to the heat conduction in the thermodynamic model, is the geometric derivative of the raycast thickness calculation with respect to the SDF; Hydrodynamic performance item gradient Calculated by the differential CFD module: Based on the gradient updating the geometric control point coordinates q using a gradient descent algorithm e .

5. The method of claim 4, wherein: The logic for repeatedly executing steps 1 to 3 to iteratively update the set of geometric control point coordinates is as follows: When the iteration is terminated, a final set of geometric control point coordinates Q is obtained final , and based on Q final , a signed distance field function SDF is reconstructed final , the zero level surface of SDF final is extracted, and a continuously derivable CAD geometric model is generated through a non-uniform rational B-spline surface fitting algorithm, the fitting residual satisfies ||SDF final (p)||<10 -5 , and the output model format is an industry standard BREP file; The iteration is terminated when any of the following stop conditions is met, and the final propeller geometric model is output: 1) The average shrinkage rate is reduced to below the target: 2) The relative loss of hydrodynamic efficiency is not more than the tolerance range, i.e. 3) The improvement amplitude of the comprehensive optimization objective function J in the last 5 iterations is less than 0.001, and 4) the total number of iterations reaches 200 times. Before the iteration is terminated, the final verification should be performed on the final generated triangular mesh surface, including: rechecking the included angle between the normal vector at all mesh vertices and the casting direction to ensure that the global demolding angle γ≥θ min ; Verify the compliance of the surface geometry with the hydrodynamic performance; generate a propeller geometric model that meets the demolding requirements and takes into account the hydrodynamic performance, which is used for subsequent detailed design and manufacturing processes.

6. A machine learning based ship propeller design optimization system, characterized by: The system is used to perform the machine learning-based ship propeller design optimization method of any one of claims 1-5, comprising: A surface construction module for constructing a parametric surface according to the set of geometric control point coordinates of the ship propeller blade, and converting it into an initial triangular mesh surface, calculating the angle between the normal vector of each grid vertex and the casting direction, identifying the vertices with an angle less than a preset demolding angle threshold, adjusting the geometric control point coordinates through a gradient optimization algorithm to drive the surface deformation, until all vertices meet the demolding angle constraint, and finally generating a triangular mesh surface; A defect calculation module for calculating the local cross-sectional thickness of the blade based on SDF, inputting the triangular mesh surface into a differential thermodynamic model to simulate the evolution of the thermal state field during casting, and inputting the thermal state field and local cross-sectional thickness into a spatiotemporal feature extraction network to output the spatial distribution of the propeller body shrinkage defect probability; An objective optimization module for synthesizing the spatial distribution of the shrinkage defect probability and the hydrodynamic performance to construct an optimization objective function, and for propagating the gradient of the optimization objective function from the thermal state field through the triangular mesh surface and the SDF to each geometric control point coordinate through a differential simulation link, and for synchronously updating all geometric control point coordinates based on gradient information using an optimization algorithm; An iterative update module for repeatedly executing steps 1 to 3 to iteratively update the set of geometric control point coordinates until the global shrinkage defect probability is less than a preset safety threshold, the loss of hydrodynamic performance is within a tolerance range, and the optimization objective function converges to a stable range, terminating the loop and outputting a propeller geometric model constructed based on the final set of geometric control point coordinates.

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