A three-dimensional induction welding coil optimization design method and related equipment

Abstract

The embodiment of the application provides a three-dimensional induction welding coil optimization design method and related equipment, and belongs to the field of advanced manufacturing and electromagnetic heating technology. The method comprises the following steps: discretizing a three-dimensional design space, defining geometric and topological constraints, and constructing a scalarization objective function; according to the obstacle layout, the homotopy class is divided, the representative curve is generated as an initial topological template; a differential homeomorphism mapping parameterized by a radial basis function network is constructed to drive the representative curve to deform geometrically; a serialization decision strategy is adopted, a fast proxy model based on the Biot-Savart law and a local gradient adaptive step are combined to iteratively optimize the deformation parameters at low cost; the candidate path is verified by high-fidelity finite element simulation, and the design meeting the engineering index and having the maximum and minimum performance margin is selected as the final result. The application significantly reduces the calculation cost while strictly guaranteeing the physical feasibility of the coil, and improves the efficiency and yield of complex structure design.

Description

Technical Field

[0001] This application relates to the fields of advanced manufacturing and electromagnetic heating technology, and in particular to a three-dimensional induction welding coil optimization design method and related equipment. Background Technology

[0002] Induction welding is a highly efficient, non-contact advanced manufacturing process, the core of which lies in the geometric design of the induction coil. The coil's topology directly determines the magnetic field distribution and heating efficiency. Traditional coil design heavily relies on engineers' experience and is typically limited to handling single, regular workpieces. With the widespread application of induction heating technology in industrial manufacturing, the geometric design of the induction coil has become a key factor determining heating efficiency and process quality. Traditional coil design, however, relies heavily on engineers' experience, is typically limited to handling regular workpieces, and requires repeated trial and error in the design process.

[0003] Existing automated design schemes for complex 3D coils mainly fall into two categories: one is optimization based on highly free discrete grids or control points, which directly searches for the coordinates of the coil path points in 3D space; the other is optimization based on parametric modeling, which predefines the geometric structure template of the coil (such as racetrack or spiral), converts it into a set of geometric parameters (such as length, width, radius, and turn spacing), and then combines surrogate models or heuristic algorithms to optimize these parameters.

[0004] However, existing technical solutions have significant shortcomings in practical applications. Existing parametric optimization methods rely heavily on the designer's prior experience to construct the initial geometric template. This method is essentially just fine-tuning the dimensions under a fixed topology and cannot achieve true topology optimization. Once the initially selected topology template cannot meet the requirements of complex physical fields, the algorithm can only operate within a limited parameter space and cannot break through the preset framework to explore novel structures with different connectivity relationships or better bypass paths. This preset limitation on the range of structural shapes greatly compresses the design space, often resulting in only locally optimal solutions, making it difficult to cope with design scenarios with complex workpiece shapes or severe multi-objective conflicts. Although directly optimizing the control point coordinates theoretically has the greatest design freedom, in high-dimensional space, coils, as entities that must be closed and conductive, must satisfy strict strong topological constraints (such as connectivity, no self-intersection, and no branches). Existing free search algorithms are prone to generating physically infeasible structures with knots, breaks, or through-the-molds, resulting in most computational resources being wasted on evaluating invalid solutions, leading to extremely low convergence efficiency. Furthermore, regardless of the scheme used, the performance evaluation of coils highly depends on time-consuming multiphysics finite element simulations. When faced with high-dimensional parameter spaces or complex topology search tasks, traditional methods usually require massive iterations to converge, resulting in excessively long computation cycles that fail to meet the industry's demand for agile design. Summary of the Invention

[0005] This application aims to overcome the problems of topological rigidity and limited exploration range in existing parametric models, difficulty in maintaining topological constraints in free space search, and high simulation computation costs. It provides a three-dimensional induction welding coil optimization design method, electronic device, storage medium, and program product. Through a two-stage strategy of "topology template selection + geometric refinement", it uses differential homeomorphism mapping to transform the optimization problem of discrete and continuous mixture into a topology-invariant continuous parameter space optimization problem. Combined with a fast physical proxy model, it significantly improves the search efficiency and finally obtains the optimal coil design that meets all engineering indicators and has the maximum performance margin.

[0006] To achieve the above objectives, one aspect of this application proposes a three-dimensional induction welding coil optimization design method, applied to the automated design of coil geometry in induction welding processes. The method includes: S1: Problem Definition and Spatial Discretization: The three-dimensional physical space to be designed is discretized into a voxel grid. The coil structure is defined as a set of conductor voxels in the voxel grid that satisfy the preset topological constraints. A scalar objective function based on the minimax criterion is constructed. The objective function is used to evaluate the heating performance of the coil. S2: Topology template generation and homotopy class construction: Based on the layout of obstacles in the design space, divide into several homotopy classes representing different winding logics, and construct a representative curve that satisfies the boundary conditions in the free space of each homotopy class as the initial topology template of the coil. S3: Construction of Environmental Space Deformation Field and Differential Homeomorphism Map: Construct a differential homeomorphism map parameterized by a radial basis function network. Drive the initial topological template to undergo geometric deformation through the differential homeomorphism map to generate a series of candidate curves. Mathematically, the deformation process ensures that the candidate curves and the initial topological template belong to the same homotopy class, thus naturally satisfying the preset topological constraints. S4: Serialization decision optimization based on physical surrogate model: The serialization decision strategy is adopted to decompose the parameter optimization process of the differential homeomorphism mapping into multiple incremental adjustment steps. In each step, the performance of the current candidate curve is evaluated based on the fast physical surrogate model, and the deformation parameters of the next step are adaptively adjusted accordingly. S5: High-fidelity simulation verification: Discretize the optimized candidate curves and map them back to voxel space, call high-fidelity simulation software to verify the performance, and calculate the true objective function value. S6: Optimal Solution Selection: From all candidate solutions verified by high-fidelity simulation, select the design solution that satisfies all engineering constraints and has the maximum and minimum performance margins as the final three-dimensional induction welding coil optimization design result.

[0007] In some embodiments, the preset topological constraints in S1 include: The conductor path strictly avoids pre-defined obstacle areas and avoidance constraints; The conductor path is a continuous and unbranched connectivity constraint from the preset current inlet to the outlet; And simple path constraints where conductor paths are not self-intersecting and all conductor voxels belong to the path.

[0008] In some embodiments, the step of constructing the representative curve in S2 specifically includes: dividing the design space into multiple distinct homotopy classes based on the net number of coil windings relative to the obstacle set; and constructing a representative curve connecting the current inlet and outlet, determined by a set of ordered control points, in the continuous free space of the selected homotopy class.

[0009] In some embodiments, the step of constructing the differential homeomorphism in S3 further includes: The differential homeomorphism mapping is defined as a flow generated by a time-varying vector field; The vector field is parameterized by using a radial basis function network, which transforms the infinite-dimensional deformation field optimization problem into a finite-dimensional optimization problem of the radial basis function weight vector.

[0010] In some embodiments, the step of constructing the differential homeomorphism in S3 further includes: Construct a spatial sensitivity scalar field that comprehensively considers geometric distance and physical field gradient; Based on the spatial sensitivity scalar field, the center point positions of the radial basis functions are dynamically and non-uniformly deployed, and adaptive kernel widths are assigned to the center points in different regions to achieve fine deformation in critical regions and macroscopic adjustment in non-critical regions.

[0011] In some embodiments, the serialization decision optimization in S4 further includes: Each decision action is defined as a triple containing the affected basis function index, deformation direction, and deformation intensity; The magnetic field distribution of the current candidate curve is calculated using a fast surrogate model based on the Biot-Savart law to evaluate the performance gain of the decision action in real time.

[0012] In some embodiments, the deformation intensity in S4 is determined using an adaptive step-size strategy based on local gradients, specifically including: Calculate the numerical gradient of the objective function of the surrogate model in the current deformation direction; If the gradient is not greater than zero, then a perturbation exploration is performed using a preset minimum step size; If the gradient is greater than zero, the deformation intensity is made to adapt to the gradient magnitude and is saturated with a preset maximum deformation intensity.

[0013] To achieve the above objectives, another aspect of this application provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method described above.

[0014] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0015] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer program product, including a computer program that, when executed by a processor, implements the method described above.

[0016] Compared with the prior art, the technical solution of this application has the following beneficial effects: 1) Significantly reduced computational costs and shorter design cycles. This application introduces a physical surrogate model based on the Biot-Savart law as an intermediate evaluation layer, greatly reducing the number of calls to expensive finite element simulations. High-fidelity simulation is used only in the final verification stage, achieving multi-precision fusion optimization of low-cost physical priors and high-precision engineering verification. Compared with traditional methods, a wider design space can be explored within the same time budget.

[0017] 2) Ensuring physical feasibility and improving design yield. This application embeds hard topological constraints such as connectivity and avoidance into the parametric expression through the definition of homotopy classes and differential homeomorphism mapping. By utilizing environmental space deformation technology, it ensures that the generated coil path is always a continuous, non-self-intersecting, and obstacle-free simple path, solving the common structural illegality problem in complex 3D winding design and significantly improving the design yield.

[0018] 3) Overcoming topological limitations and improving performance ceiling. This application no longer relies on traditional helical or racetrack-shaped fixed templates, but instead reconstructs the design space based on underlying topological features. Through a two-stage strategy of "topology template selection + geometric refinement," it can freely explore complex spatial morphologies while satisfying specific winding logic. This enables the algorithm to discover high-performance irregular coil structures that traditional experience cannot predict and that parameterized templates cannot express, significantly improving the performance ceiling of the design.

[0019] 4) High optimization efficiency and good convergence performance. This application decomposes global synchronous optimization into a series of local incremental adjustment steps through serial decision-making, which greatly reduces the space complexity of a single search. Combined with an adaptive step size adjustment strategy based on local gradients, it ensures the accuracy of the search direction and avoids oscillations or slow convergence caused by excessively large or small step sizes, enabling the algorithm to quickly lock onto and approach the optimal solution.

[0020] 5) Rational utilization of computational resources. This application constructs a spatial sensitivity scalar field and dynamically allocates the density of RBF kernel function center points based on geometric distance and physical field gradient: densely deployed in bottleneck areas and sparsely deployed in open areas, and assigns differentiated action radii to control points in different regions. This solves the problem of wasted computing power caused by traditional uniform point distribution, and achieves efficient utilization of computational resources and decoupled optimization of multi-scale geometric features. Attached Figure Description

[0021] Figure 1 This is a flowchart of the three-dimensional induction welding coil optimization design method provided in the embodiments of this application; Figure 2 This is a flowchart of the three-dimensional induction welding coil optimization design method based on differential homeomorphism and sequential intelligent decision-making provided in the embodiments of this application; Figure 3 This is a schematic diagram of the three-dimensional induction welding coil optimization design method based on differential homeomorphism and sequential intelligent decision-making provided in the embodiments of this application; Figure 4 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit it. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this application; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the appended claims.

[0023] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0024] Before providing a detailed description of the embodiments of this application, some of the nouns and terms involved in the embodiments of this application will be explained first. The nouns and terms involved in the embodiments of this application are subject to the following interpretations.

[0025] 1) Induction welding is a process that uses high-frequency electromagnetic fields to generate heat to join materials. It mainly uses metal inserts, metal mesh, hot-pressed metal foil or metal powder resin mixture as heating elements. The eddy current resistance generated by electromagnetic induction or the hysteresis effect melts the thermoplastic matrix, and the connection structure is formed after cooling.

[0026] 2) Differeomorphism, a mathematical term, refers to the concept of isomorphism applicable to the category of differentiable manifolds. It is an invertible mapping between differentiable manifolds such that both the mapping and its inverse are smooth (i.e., infinitely differentiable).

[0027] To address the problems existing in the prior art, this application proposes a three-dimensional induction welding coil optimization design method, electronic device, storage medium, and program product based on differential homeomorphism and sequential intelligent decision-making. This scheme first discretizes the three-dimensional design space, defines strict geometric and topological constraints, and establishes a scalarized objective function based on the minimax criterion. Next, a set of homotopy classes is constructed based on the obstacle layout, generating representative curves that satisfy specific winding logic as initial topological templates. Subsequently, an environmental space deformation strategy is introduced, combined with a spatial attention mechanism for adaptive node deployment, constructing a parameterized vector field based on radial basis functions (RBF). Differential homeomorphism mapping drives geometric refinement of the representative curves, mathematically ensuring that the topological features remain unchanged throughout the optimization process. In the optimization stage, a sequential decision-making strategy is adopted, combining a fast surrogate model based on the Biot-Savart law and a local gradient adaptive step size for low-cost evaluation and search. Finally, high-fidelity finite element simulation is performed on the selected candidate paths, and the design that meets all engineering indicators and has maximum and minimum performance margins is selected as the final result. This invention effectively overcomes the problems of rigid topology and limited exploration range of traditional parametric models. While strictly ensuring the feasibility of the coil's physical topology, it significantly reduces computational costs and improves the efficiency and yield of complex structure design.

[0028] The three-dimensional induction welding coil optimization design method provided in this application relates to the fields of advanced manufacturing and electromagnetic heating technology. This method can be applied to terminals, servers, or software running on either a terminal or server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, or vehicle terminal, but is not limited to these. The server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network. The software can be an application implementing the three-dimensional induction welding coil optimization design method, but is not limited to the above forms.

[0029] This application can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0030] like Figure 1 As shown, this embodiment provides a three-dimensional induction welding coil optimization design method, which is applied to the automated design of coil geometry in induction welding processes. The method specifically includes the following steps: Step S101: Problem definition and spatial discretization: Discretize the three-dimensional design space into a voxel grid, define the coil structure as a set of conductor voxels in the voxel grid that satisfy the preset topological constraints, and construct a scalarized objective function based on the minimax criterion; Step S102: Topology template generation and homotopy class construction: Based on the layout of obstacles in the design space, divide into several homotopy classes representing different entanglement logics, and construct a representative curve that satisfies the boundary conditions in the free space of each homotopy class as the initial topology template. Step S103: Construction of environmental space deformation field and differential homeomorphism: Construct a differential homeomorphism parameterized by radial basis function network, drive the initial topology template to perform geometric deformation through the differential homeomorphism, and generate a series of candidate curves. The deformation process mathematically guarantees that the candidate curves and the initial topology template belong to the same homotopy class, thus naturally satisfying the preset topology constraints. Step S104: Serialization decision optimization based on physical surrogate model: The serialization decision strategy is adopted to decompose the parameter optimization process of the differential homeomorphism mapping into multiple incremental adjustment steps. In each step, the performance of the current candidate curve is evaluated based on the fast physical surrogate model, and the deformation parameters of the next step are adaptively adjusted accordingly. Step S105: High-fidelity simulation verification: Discretize the optimized candidate curves and map them back to voxel space, call high-fidelity simulation software to verify the performance, and calculate the true objective function value. Step S106: Optimal solution selection: From all candidate solutions that have been verified by high-fidelity simulation, select the design solution that satisfies all engineering constraints and has the maximum and minimum performance margins as the final optimization result.

[0031] The solutions of the embodiments of this application will be described in detail below with reference to the accompanying drawings and specific application examples.

[0032] To overcome the problems of topological rigidity and limited exploration range in existing parametric models, difficulty in preserving topological constraints in free space search, and high simulation computation costs, this embodiment proposes a three-dimensional induction welding coil optimization design method based on differential homeomorphism and sequential intelligent decision-making. This method employs a two-stage strategy of "topology template selection + geometric refinement," utilizing differential homeomorphism to transform the mixed discrete and continuous optimization problem into a topologically invariant continuous parameter space optimization problem, and significantly improves search efficiency by combining a fast physical surrogate model. See also... Figure 2 and Figure 3 The method specifically includes the following six steps: Step S1: Problem definition and spatial discretization.

[0033] S1-1: First, in order to transform the continuous physical space into a computable mathematical model, this embodiment discretizes the three-dimensional space to be designed into a uniform voxel mesh. In this grid system, any location in space can be indexed by its integer value. A unique identifier, formally defined as follows:

[0034] in, They represent the design space in Voxel resolution in three directions.

[0035] S1-2: Based on this, the single coil structure Defined as a subset of voxels in space, and formalized as a binary mapping function to indicate whether a voxel is filled with a conductive material:

[0036] Specifically, when When, it indicates that the voxel is a conductor; when When the value is 0, it indicates that the voxel is a nonconductor (i.e., vacuum or air).

[0037] S1-3: To ensure the physical feasibility of the generated coil, the design solution must simultaneously satisfy the following three strict constraints: 1) Avoidance constraint: conductor path Areas where clothing is prohibited must be strictly avoided. (e.g., the workpiece to be welded), that is:

[0038] 2) Connectivity constraints: Structure All marked as The voxels must form a current path from the preset current inlet s to the outlet. continuous path :

[0039] 3) Simple path constraints: To prevent physical short circuits, the path... Self-intersection is not allowed, and All conductor voxels must belong to this path:

[0040] S1-4: To address the multi-objective optimization problem, this invention employs a minimax strategy for scalarization. Specifically, the objective function is defined as follows: This refers to the margin of the key performance indicator (KPI) that has the largest difference from its preset performance target among all KPIs. Let the margin of each performance indicator be... Then the objective function is defined as:

[0041] This function aims to maximize the aforementioned minimum value, thereby prioritizing the improvement of the system's weakest link performance and ensuring high reliability of the design results.

[0042] Step S2: Topology template generation and homotopy class construction.

[0043] S2-1: To address the issue of diverse topologies, this embodiment is based on the coil relative to the set of obstacles. The net winding number divides the design space into several distinct sets of homotopy classes. Each homotopy class Each of these represents a unique winding logic.

[0044] S2-2: For any chosen homotopy class In continuous free space where obstacles are eliminated In the middle, construct a representative curve that satisfies this topological feature. :

[0045] The curve consists of an ordered sequence of control points. Uniquely determined and satisfying boundary conditions and As an initial topology template for subsequent geometry optimization, this curve ensures basic connectivity and bypass relationships.

[0046] Step S3: Construct the environmental spatial deformation field and differential homeomorphism mapping.

[0047] S3-1: To strictly maintain topological properties during geometric refinement, this embodiment abandons the traditional method of directly modifying curve coordinates and instead introduces an environment space deformation strategy. Specifically, a differential homeomorphism mapping from continuous space to itself is defined. The final optimized curve From the initial representative curve The result obtained through this mapping transformation is:

[0048] because It possesses the mathematical properties of being continuous and reversible; the transformed curve Inevitably and They belong to the same homotopy class, thus naturally satisfying all the topological constraints defined in S1-3.

[0049] S3-2: Further, the mapping Defined as a time-varying vector field The generated stream. Any point in space. With virtual time The evolution follows ordinary differential equations:

[0050] To transform an infinite-dimensional deformable field into an optimizable finite-dimensional problem, a radial basis function (RBF) network is used for the vector field. Perform parameterized approximation:

[0051] in, Let be a Gaussian kernel basis function. Let be the weight vector. Thus, the complex curve shape optimization problem is transformed into optimizing the set of parameter vectors. The optimization problem.

[0052] S3-3: To address the computational waste caused by uniformly deploying control points and to achieve multi-scale decoupling, this embodiment constructs a spatial sensitivity scalar field. This field comprehensively considers geometric distance (higher weight for closer objects) and physical field gradient (higher weight for more drastic changes in the initial proxy magnetic field). Based on this sensitivity field, the algorithm dynamically and non-uniformly allocates the aforementioned... The RBF basis functions are densely deployed in the high-weight slit bottleneck region and sparsely deployed in the outer open region. At the same time, nodes with different densities are given adaptive action radii (kernel widths): large kernel functions are used in sparse regions for global macroscopic contour coarse adjustment, and small kernel functions are used in dense regions for local microscopic fine avoidance, thus achieving decoupled optimization of multi-scale geometric features.

[0053] Step S4: Serialization decision optimization based on physical agent model.

[0054] S4-1: To efficiently search for optimal parameters In this embodiment, global optimization is decomposed into a series of sequential local incremental adjustment processes. In the first... In the iterative process, decision-making actions It is defined as a triple containing region, direction, and intensity:

[0055] in The affected base function indices are specified. For the direction of deformation, This represents the deformation intensity. The corresponding parameter update rules follow:

[0056] S4-2: Considering the high cost of finite element simulation, this embodiment utilizes the Biot-Savart law to construct a fast surrogate objective function. For any candidate coil curve Its spatial point The magnetic induction intensity generated at the location The following formula can be used for quick estimation:

[0057] Based on this formula, the algorithm can quickly calculate the magnetic field distribution in key areas, providing real-time feedback signals for the optimization process.

[0058] S4-3: Determining the deformation intensity In this embodiment, an adaptive strategy is used instead of random search. A proxy target is utilized. To obtain local gradient information, we first calculate an approximate numerical gradient:

[0059] based on The symbol and size determine the stride. : like This means that continuing in the current direction will not improve [the situation]. It may even decrease. To ensure a certain degree of exploration without excessively disrupting the existing geometry, this embodiment only takes the minimum step size in this direction:

[0060] like This indicates that increasing deformation along the current direction is beneficial for improving the agent target. At this point, the intensity is made to adapt to the gradient magnitude. To avoid deformation distortion or numerical instability caused by excessively large step sizes, a maximum deformation intensity is introduced. In saturated form:

[0061] in This is a scaling factor that maps the gradient magnitude to the deformation intensity. Thus, when... Smaller values ​​correspond to smaller deformations, when When it is large, it gradually approaches the upper limit. .

[0062] In summary, the intensity selection strategy adopted in this section can be written as:

[0063] Step S5: High-fidelity simulation verification.

[0064] After the optimization iteration in step S4, a set of candidate parameters will be obtained. and its corresponding continuous curve Subsequently, Discretize and map back to voxel space The final verification is performed using high-fidelity finite element simulation software (such as Ansys Maxwell). This involves accurately calculating real physical properties (such as losses). ,inductance (etc.), and derive the true objective function value according to the formula in S1-4. .

[0065] Step S6: Optimal solution selection based on the minimax criterion.

[0066] Finally, a solution set is constructed by collecting all candidate solutions that have been verified through simulation. The final optimal design It will be selected from this set, and must meet the following conditions. And it has the largest minimum performance margin:

[0067] In summary, the method proposed in this application differs from the prior art in the following ways: 1) At the design space and modeling level, existing parametric modeling methods heavily rely on pre-defined geometric templates (such as spirals or racetracks). Their optimization process is essentially limited to fine-tuning geometric dimensions within a fixed topological framework, making it impossible to break through the structural constraints of the pre-defined templates to explore solutions with novel winding logic. In contrast, this application innovatively introduces the concept of homotopy, reconstructing the design space into a function space based on underlying topological features. By selecting a topological template and using environmental space deformation technology to drive geometric evolution, it completely breaks free from the rigid constraints of traditional geometric parameters, thereby achieving true joint optimization of topology and geometry within a broader solution space.

[0068] 2) Regarding constraint handling mechanisms, existing technologies typically have to incorporate connectivity and avoidance constraints as penalty terms into the objective function, leading to complex optimization surfaces and extremely difficult convergence. This application, however, embeds these rigid topological constraints into the parameterized expression through the definition of homotopy classes and differential homeomorphisms, ensuring that any solution generated by the algorithm naturally satisfies physical feasibility mathematically, without requiring additional penalty mechanisms.

[0069] 3) In terms of optimization and evaluation strategies, existing technologies often rely directly on expensive finite element simulations for the entire process search, which is extremely inefficient. This application adopts a hierarchical strategy of "topological template coarse search + geometric refinement" and introduces a physical surrogate model based on the Biot-Savart law to replace most of the simulation calculations. High-fidelity simulation is only used in the final verification stage, realizing multi-precision fusion optimization of low-cost physical priors and high-precision engineering verification.

[0070] This application significantly reduces the number of calls to expensive finite element simulations by introducing the Biot-Savart law, a physical proxy model, as an intermediate evaluation layer. Compared to traditional methods, it can explore a wider design space within the same time budget. Secondly, by utilizing environmental space deformation technology, it ensures that the generated coil paths are always continuous, non-self-intersecting, and simple paths that do not cross obstacles, solving the structural illegality problem commonly found in complex 3D winding designs and significantly improving design yield. Thirdly, by freeing itself from the rigid constraints of parametric models on geometry, this application can freely explore complex spatial morphologies while satisfying specific winding logic. This enables the algorithm to discover high-performance irregular coil structures that traditional experience cannot predict and that parametric templates cannot express, significantly raising the upper limit of design performance.

[0071] In summary, this application has the following advantages and beneficial effects compared to the prior art: 1) A hierarchical optimization strategy of "topology selection + geometry refinement": This strategy decouples the complex 3D coil design into two stages: first, determining the winding logic (homotopy class), and then performing continuous shape adjustments. This hierarchical strategy effectively reduces the difficulty of searching in high-dimensional space and avoids the problem of traditional methods getting stuck in incorrect topologies.

[0072] 2) A free exploration mechanism that breaks through the limitations of preset geometric templates: Instead of relying on traditional helical or racetrack-shaped fixed templates, the design space is reconstructed based on underlying topological features. This allows the algorithm to freely explore complex irregular structures, significantly expanding the design scope and discovering high-performance coil forms that traditional experience cannot cover.

[0073] 3) A self-guaranteed physical feasibility method without penalty terms: By embedding connectivity and avoidance constraints into the deformation process through differential homeomorphism, any generated solution naturally satisfies physical feasibility. This reduces the difficulty of constraint handling, eliminates the convergence difficulties caused by complex penalty terms in traditional methods, and significantly improves optimization efficiency.

[0074] 4) Winding logic classification method based on "net number of turns": Utilizing the "net number of turns" of the coil relative to the workpiece, a wide range of winding methods are divided into distinct categories. This enables effective classification and filtering of complex winding logic, providing clear topology guidance for automated design.

[0075] 5) Differential-driven continuously smooth shaping method: The deformation process of the coil is defined as a vector field flowing with virtual time, so that the change in the coil shape follows a smooth differential equation. This achieves fine and continuous adjustment of the geometry, avoiding the abrupt changes and instability caused by discrete operations.

[0076] 6) Dimensionality Reduction Parameterization Method for Deformation Fields Based on RBF Networks: This method utilizes radial basis functions (RBF) to transform the infinite-dimensional spatial deformation problem into an optimization problem with a finite number of parameters. While preserving the degrees of freedom in deformation, it significantly reduces the computational dimensionality, making the optimization of complex curves computationally feasible and efficient.

[0077] 7) Simplified Serialized Incremental Optimization Process: The global synchronous optimization is decomposed into a series of local incremental adjustment steps. This serialized decision-making greatly reduces the space complexity of a single search, enabling the algorithm to quickly lock onto and approximate the optimal solution.

[0078] 8) “Region-Direction-Intensity” Triad Decision Control Mechanism: It creatively defines decision actions that include “area of ​​action, deformation direction, and deformation intensity”, enabling precise control of the local shape of the coil and making the optimization process more targeted and interpretable.

[0079] 9) Adaptive step size adjustment strategy based on local gradients: This strategy abandons blind random search and dynamically adjusts the deformation intensity using gradient information from the surrogate model. This ensures the accuracy of the search direction and avoids oscillations or slow convergence caused by excessively large or small step sizes.

[0080] 10) A saturated update mechanism that balances exploration and convergence: A special step-size logic is designed: acceleration is achieved when the gradient direction is clear, while small-scale exploration is maintained when the gradient is unclear. This mechanism perfectly balances global search capability and local convergence speed, improving the robustness of the algorithm.

[0081] 11) Fast physical surrogate models to replace expensive simulations: A fast surrogate model is constructed using the Biot-Savart law to estimate the magnetic field distribution in key areas in real time. This provides low-cost physical prior feedback for massive searches, significantly reduces reliance on time-consuming finite element simulations, and significantly shortens the design cycle.

[0082] 12) Adaptive deployment of control nodes: The density of RBF kernel function center points is dynamically allocated based on geometric distance and physical field gradient: densely deployed in bottleneck areas and sparsely deployed in open areas. This solves the problem of wasted computing power caused by traditional uniform node deployment and achieves efficient utilization of computing resources.

[0083] 13) Global and local decoupling optimization strategy based on adaptive kernel width: Differentiated radius of action (kernel width) is assigned to control points in different regions: large kernel width is responsible for coarse adjustment of the overall contour, and small kernel width is responsible for fine local avoidance, realizing the decoupling of multi-scale geometric features and solving the problem of optimizing the details of complex structures.

[0084] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0085] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0086] Please see Figure 4 , Figure 4 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes: The processor 401 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this application. The memory 402 can be implemented as a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). The memory 402 can store the operating system and other applications. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 402 and is called and executed by the processor 401 using the methods described in the embodiments of this application. Input / output interface 403 is used to implement information input and output; The communication interface 404 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.). Bus 405 transmits information between various components of the device (e.g., processor 401, memory 402, input / output interface 403, and communication interface 404); The processor 401, memory 402, input / output interface 403 and communication interface 404 are connected to each other within the device via bus 405.

[0087] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0088] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0089] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0090] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0091] It is understood that the content of the above method embodiments is applicable to the embodiments of this program product. The specific functions implemented in the embodiments of this program product are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments. The executable computer program code or "code" used to perform the various embodiments can be written in high-level programming languages ​​such as C, C++, Python, Smalltalk, Java, JavaScript, Visual Basic, Structured Query Language (e.g., Transact-SQL), Perl, or in various other programming languages.

[0092] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0093] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0094] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0095] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0096] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0097] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0098] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0099] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, 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.

[0100] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0101] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0102] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A method for optimizing the design of a three-dimensional induction welding coil, characterized in that, The method includes the following steps: S1: Problem Definition and Spatial Discretization: Discretize the three-dimensional design space into a voxel grid, define the coil structure as a set of conductor voxels in the voxel grid that satisfy the preset topological constraints, and construct a scalarized objective function based on the minimax criterion; S2: Topology template generation and homotopy class construction: Based on the layout of obstacles in the design space, divide into several homotopy classes representing different entanglement logics, and construct a representative curve that satisfies the boundary conditions in the free space of each homotopy class as the initial topology template. S3: Construction of Environmental Space Deformation Field and Differential Homeomorphism Map: Construct a differential homeomorphism map parameterized by a radial basis function network. Drive the initial topological template to undergo geometric deformation through the differential homeomorphism map to generate a series of candidate curves. Mathematically, the deformation process ensures that the candidate curves and the initial topological template belong to the same homotopy class, thus naturally satisfying the preset topological constraints. S4: Serialization decision optimization based on physical surrogate model: The serialization decision strategy is adopted to decompose the parameter optimization process of the differential homeomorphism mapping into multiple incremental adjustment steps. In each step, the performance of the current candidate curve is evaluated based on the fast physical surrogate model, and the deformation parameters of the next step are adaptively adjusted accordingly. S5: High-fidelity simulation verification: Discretize the optimized candidate curves and map them back to voxel space, call high-fidelity simulation software to verify the performance, and calculate the true objective function value. S6: Optimal solution selection: From all candidate solutions that have been verified by high-fidelity simulation, select the design solution that satisfies all engineering constraints and has the maximum and minimum performance margins as the final optimization result.

2. The method according to claim 1, characterized in that, The preset topology constraints in S1 include: The conductor path avoids pre-defined obstacle zones and avoidance constraints. The conductor path is a continuous and unbranched connectivity constraint from the preset current inlet to the outlet; And simple path constraints where conductor paths are not self-intersecting and all conductor voxels belong to the path.

3. The method according to claim 1, characterized in that, The steps of constructing the representative curve in S2 specifically include: dividing the design space into multiple distinct homotopy classes based on the net number of coil windings relative to the obstacle set; and constructing a representative curve that connects the current inlet and outlet, determined by a set of ordered control points, in the continuous free space of the selected homotopy class.

4. The method according to claim 1, characterized in that, The step of constructing the differential homeomorphism mapping in S3 further includes: The differential homeomorphism mapping is defined as a flow generated by a time-varying vector field; The vector field is parameterized by using a radial basis function network, which transforms the infinite-dimensional deformation field optimization problem into a finite-dimensional optimization problem of the radial basis function weight vector.

5. The method according to claim 4, characterized in that, The step of constructing the differential homeomorphism in S3 further includes: Construct a spatial sensitivity scalar field that comprehensively considers geometric distance and physical field gradient; Based on the spatial sensitivity scalar field, the center point positions of the radial basis functions are dynamically and non-uniformly deployed, and adaptive kernel widths are assigned to the center points in different regions to achieve fine deformation in critical regions and macroscopic adjustment in non-critical regions.

6. The method according to claim 1, characterized in that, The serialization decision optimization in S4 further includes: Each decision action is defined as a triple containing the affected basis function index, deformation direction, and deformation intensity; The magnetic field distribution of the current candidate curve is calculated using a fast surrogate model based on the Biot-Savart law to evaluate the performance gain of the decision action in real time.

7. The method according to claim 6, characterized in that, The deformation intensity in S4 is determined using an adaptive step-size strategy based on local gradients, specifically including: Calculate the numerical gradient of the objective function of the surrogate model in the current deformation direction; If the gradient is not greater than zero, then a perturbation exploration is performed using a preset minimum step size; If the gradient is greater than zero, the deformation intensity is made to adapt to the gradient magnitude and is saturated with a preset maximum deformation intensity.

8. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method according to any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 7.

Images