A dot matrix structure optimization design method based on NURBS curve and machine learning

Abstract

The application discloses a lattice structure optimization design method based on NURBS curves and machine learning, and comprises the following steps: lattice structure parameterized modeling based on periodic NURBS curves; applying periodic boundary conditions and homogenization processing; construction and training of a neural network proxy model; structure parameter optimization based on a multi-objective genetic algorithm, and output of a Pareto optimal solution set, wherein the Pareto optimal solution set is an optimal design scheme. The application defines a strut section shape through periodic NURBS curves, combines a neural network proxy model and a multi-objective optimization algorithm, and efficiently designs a lattice structure with high efficient Young's modulus in a target direction and minimum volume (or relative density). The application has the following advantages: the application can flexibly describe highly complex and continuously changing non-circular section strut geometries, efficiently realizes a design framework of coupling optimization of the geometries and target mechanical properties, and overcomes the problem that a traditional parameterized method and high-cost FEA simulation are difficult to support high degree of freedom design requirements.

Description

Technical Field

[0001] This invention relates to the field of structural topology optimization technology, specifically to a lattice structure optimization design method based on NURBS curves and machine learning. Background Technology

[0002] Current research on lattice structure optimization mainly revolves around three dimensions: truss spatial arrangement optimization, node geometric reinforcement, and column form innovation. Among them, the truss spatial arrangement optimization method has low material utilization efficiency; the node geometric reinforcement method can only alleviate the node failure problem; and the current design space for column form innovation is limited, and it cannot fully utilize the potential of additive manufacturing to explore lattice structure forms with better performance or unique functions.

[0003] Currently, the design of most struts in lattice structures is still limited to uniform diameter or simple conical variations on a circular cross-section (solid or hollow). This restriction on the basic cross-sectional shape (circular) severely constrains design freedom. Furthermore, the performance prediction and optimization of current lattice structures heavily rely on computationally intensive finite element analysis (FEA). When the number of design variables increases or high-dimensional global optimization is required, the computational cost becomes extremely high and inefficient, becoming a bottleneck for performance breakthroughs. In addition, existing strut morphology designs for lattice structures (such as tapering and spherical nodes) mainly rely on empirical formulas or predefined geometric transformations, lacking the ability to perform adaptive, nonlinear morphological optimization based on the actual stress field. Summary of the Invention

[0004] The purpose of this invention is to provide a lattice structure optimization design method based on NURBS curves and machine learning, which aims to overcome the problems in the prior art such as limited lattice structure support shape design, high performance prediction and optimization computation costs, and difficulty in achieving global optimization in high-dimensional parameter space.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for optimizing the design of lattice structures based on NURBS curves and machine learning includes the following steps: S1. Parametric modeling of lattice structures based on periodic NURBS curves: Generating lattice structures with periodic variable cross-section supports using periodic NURBS curves. S2. Apply periodic boundary conditions and homogenization: Using the lattice structure generated in S1 as a representative volume element, apply periodic boundary conditions and homogenization analysis to it, and calculate its equivalent Young's modulus and volume. S3. Construction and training of neural network surrogate models: A multilayer perceptron neural network model is established as a surrogate model for the equivalent Young's modulus and volume of the lattice structure in S2, and the constructed neural network surrogate model is trained; the neural network surrogate model includes a neural network surrogate model for the equivalent Young's modulus of the lattice structure and a neural network surrogate model for the volume of the lattice structure. S4. Structural parameter optimization based on multi-objective genetic algorithm: Establish a multi-objective optimization problem with the objectives of maximizing the equivalent Young's modulus in the target direction and minimizing the volume or equivalently minimizing the relative density. Solve the problem using a multi-objective genetic algorithm and output the Pareto optimal solution set. The Pareto optimal solution set is the optimal design scheme of the representative volume unit in S2.

[0006] Furthermore, the feature is that S1 specifically includes: S101. Create a periodic NURBS curve: Select a p-order NURBS curve; set a uniform node vector; set n independent control points and distribute the n control points equally in a circle in a two-dimensional plane, with the first control point coinciding with the last control point; independently set the weight value of each control point and constrain the weight value of each control point between 0 and 1; where p is the order of the NURBS curve and > 1; S102. Constructing the column cross-section: First, set m cross-section positions along the 1 / 2 axis of the column, and apply the periodic NURBS curve created in S101 to each cross-section position to generate a periodic closed cross-section profile. The periodic closed cross-section profile generated at each cross-section position is the cross-section profile shape of the column at that cross-section position. Then, generate multiple periodic closed cross-section profiles along the other 1 / 2 axis of the column through the mirror mapping principle, thereby obtaining a complete cross-section cluster distributed along the axis of the column; where m > 1. S103, 3D Reconstructed Column: In computer-aided design software, the lofting function is used to connect the complete cross-section clusters distributed along the column axis obtained in S102, and reconstruct a single 3D column entity with a smooth transition variable cross-section. S104. Construct a complete lattice structure: First, position the single three-dimensional pillar entity generated in S101 to the corresponding position of the lattice structure through rigid body transformation. Then, generate a standard spatial array structure through rotation array and mirror transformation operations. Finally, perform a topology merging operation to form a complete lattice structure with periodic variable cross-section pillars.

[0007] Furthermore, the feature is that S2 specifically includes: S201. Using the single lattice structure generated in S1 as a representative volume element, periodic boundary conditions are applied to it in the finite element analysis software. The boundary nodes of the representative volume element are bound to the reference node degrees of freedom through constraint equations to simulate the periodic repetition characteristics of the lattice structure in space and analyze the mechanical response of the complete lattice material. The expression of the constraint equations is as follows: in, The microscopic field variables that need to be solved, These are the coordinates of a node on the boundary of a representative volume element. It is the ❛�th periodic vector. Microscopic field variables The macroscopic far-field gradient; S202. Under the set macroscopic strain drive, the equivalent elastic tensor of the representative volume element is calculated using the volume averaging algorithm, and the equivalent Young's modulus in the target direction is extracted.

[0008] Furthermore, the feature is that the neural network proxy model constructed in S3 is a multilayer perceptron neural network model, and its input parameters are the geometric design parameters of the support column, namely the radius of the control point distribution circle of all independent sections of the support column. and independent weighting factors The output parameter is the equivalent Young's modulus of a representative volume element. and volume .

[0009] Furthermore, both the neural network proxy model for the equivalent Young's modulus of the lattice structure and the neural network proxy model for the volume of the lattice structure adopt a double hidden layer structure.

[0010] Furthermore, the training of the neural network surrogate model in S3 specifically employs the backpropagation algorithm.

[0011] Furthermore, the specific steps for training the neural network surrogate model in S3 are as follows: S301. Data Generation: First, a large number of sample points are uniformly generated in the high-dimensional design parameter space using the Latin hypercube sampling method, where the parameter space range is... , Then, for each sample point, parametric modeling is first performed using method S1, and then periodic boundary conditions and homogenization analysis are applied using method S2 to calculate its corresponding equivalent Young's modulus and volume, forming a structured dataset. S302, Model Training: First, the structured dataset generated in S301 is divided into a training set, a validation set, and a test set, with the training set accounting for 80%, the validation set accounting for 10%, and the test set accounting for 10%. Then, the training set is substituted into the neural network proxy model, and the neural network proxy model is trained using the error backpropagation algorithm.

[0012] Furthermore, S4 specifically includes: S401. Establish the equivalent Young's modulus in the target direction to maximize the target direction. and minimize volume Or equivalently minimize relative density The mathematical formulation of the multi-objective optimization problem with objective T is as follows: in, The radius of the circle used to distribute control points; The weighting factor for the control points; Equivalent Young's modulus; For volume; Number of cross sections; Number of control points; S402. A multi-objective genetic algorithm is used to solve the multi-objective optimization problem established in S402, and the Pareto optimal solution set is output. The optimal solution set is the optimal design scheme of the representative volume unit in S2.

[0013] Compared with existing technologies, the lattice structure optimization design method based on NURBS curves and machine learning provided by this invention can not only flexibly describe the highly complex and continuously changing geometry of non-circular cross-section pillars, but also efficiently achieve coupled optimization with the target mechanical properties, effectively overcoming the problem that traditional parametric methods and high-cost FEA simulations cannot support high-degree-of-freedom design requirements.

[0014] Compared with existing technologies, the lattice structure optimization design method based on NURBS curves and machine learning provided by this invention has achieved significant breakthroughs in terms of technical performance, computational efficiency, manufacturing applicability, and economic benefits, as detailed below: 1. Technical performance Significantly enhanced mechanical properties: The BCC lattice structure optimized by the method of this invention has a significantly improved equivalent Young's modulus in the Y direction compared with the traditional BCC lattice structure at the same relative density. Especially at low relative density (ρ=0.211), the modulus is improved by up to 144.8%, breaking through the performance limit of lightweight structures.

[0015] 2. Computational efficiency By employing an MLP neural network surrogate model (with a dual hidden layer structure) to replace traditional finite element analysis, the time required for a single performance prediction is reduced from minutes to seconds; the model's prediction accuracy for equivalent Young's modulus and volume reaches R0. 2 >0.996, which meets the requirements for engineering optimization.

[0016] 3. Manufacturing applicability Parametric design supports customization: By adjusting the control point distribution radius and weight factor, the cross-sectional shape of the support column (such as prismatic protrusions and tapered gradients) can be flexibly adjusted to adapt to different mechanical scenario requirements (such as energy absorption and impact resistance).

[0017] 4. Economic benefits Lightweight and material savings: With the same modulus requirements, the relative density is lower, directly reducing the amount of high-cost materials (such as Ti-6Al-4V) used.

[0018] The innovation of this invention is that by defining the cross-sectional shape of the support column through periodic NURBS (Non-Uniform Rational B-Spline) curves, and combining a neural network surrogate model and a multi-objective optimization algorithm, a lattice structure with high equivalent Young's modulus and minimum volume (or relative density) in the target direction can be efficiently designed. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in this embodiment, the accompanying drawings used in the description of the embodiment will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart of the lattice structure optimization design method based on NURBS curves and machine learning of the present invention; Figure 2 This is a schematic diagram of the parameters for creating periodic NURBS curves according to the present invention; Figure 3 This is a schematic diagram of the construction process of the BCC lattice structure variable cross-section support column involved in this invention; Figure 4 This is a schematic diagram of the BCC lattice structure generation process involved in the present invention; Figure 5 This is a schematic diagram of the BCC lattice structure optimization process involved in the present invention; Figures 6-8 The images show stress-strain curves of BCC lattice structures generated by conventional methods and BCC lattice structures generated by the method of this invention at different densities. Figure 9This is a comparison chart of the elastic moduli of BCC lattice structures generated by conventional methods and BCC lattice structures generated by the method of this invention. Detailed Implementation

[0021] To make the technical means, creative features, objectives and effects of this invention easier to understand, the following description, in conjunction with the accompanying drawings and specific embodiments, further explains how this invention is implemented.

[0022] See Figure 1 The present invention provides a lattice structure optimization design method based on NURBS curves and machine learning, comprising the following steps: S1. Parametric modeling of lattice structures based on periodic NURBS curves: that is, using periodic NURBS curves to generate lattice structures with periodic variable cross-section supports. The purpose of step S1 is to break through the limitations of traditional lattice structure pillars with uniform cross-sections or simple linear cone shapes. By utilizing the local controllability and high-order continuity of NURBS curves, it achieves arbitrary, smooth, and precise parametric control of the pillar cross-section shape in a two-dimensional plane. Through the definition of multiple axial cross-sections, it realizes complex gradient changes in the overall three-dimensional shape of the pillar (such as taper, protrusion, etc.), which greatly expands the design freedom of lattice structures and lays the foundation for subsequent performance optimization.

[0023] S2. Apply periodic boundary conditions and homogenization: The lattice structure generated in S1 is used as a representative volume element. Periodic boundary conditions and homogenization analysis are applied to it to calculate its equivalent Young's modulus and volume. The purpose of step S2 is to ensure accurate prediction of the macroscopic equivalent elastic properties (especially the equivalent Young's modulus) of the entire periodic lattice structure on a smaller lattice structure model by applying periodic boundary conditions. This significantly reduces the computational cost of large-scale structural simulation and provides crucial support for efficient generation of training data and performance verification. Homogenization analysis establishes a direct relationship between microscopic cell geometric parameters and macroscopic equivalent properties.

[0024] S3. Construction and training of neural network surrogate models: This involves establishing a multilayer perceptron neural network model as a surrogate model for the equivalent Young's modulus and volume of the lattice structure in S2. This includes a neural network surrogate model for the equivalent Young's modulus of the lattice structure and a neural network surrogate model for the volume of the lattice structure. The constructed neural network surrogate models for the equivalent Young's modulus of the lattice structure and the neural network surrogate models for the volume of the lattice structure are then trained. The purpose of step S3 is to quickly predict the equivalent Young's modulus and volume values ​​under a given combination of geometric parameters with extremely low computational cost when constructing a neural network surrogate model and using the trained neural network surrogate model to calculate the equivalent Young's modulus and volume. This solves the key bottleneck of repeatedly calling high-cost simulation models in the process of multi-objective optimization, making it possible to efficiently explore high-dimensional design spaces.

[0025] S4. Structural parameter optimization based on multi-objective genetic algorithm: This involves establishing a multi-objective optimization problem with the objectives of maximizing the equivalent Young's modulus in the target direction and minimizing the volume or equivalently minimizing the relative density. The multi-objective genetic algorithm is used to solve the problem, and the Pareto optimal solution set is output. The Pareto optimal solution set is the optimal design scheme of the representative volume unit in S2.

[0026] The purpose of step S4 is to effectively handle multi-objective, high-dimensional, and nonlinear optimization problems through multi-objective genetic algorithms and to find well-distributed Pareto optimal solution sets in the solution space. Combined with a neural network surrogate model, it greatly improves optimization efficiency (reducing computation time from several days to several hours), making it possible to perform global optimization in a high-dimensional space containing dozens of design variables, thereby finding a combination of N-BCC structural parameters with excellent comprehensive performance (high modulus / lightweight).

[0027] Specifically, the lattice structure optimization design method based on NURBS curves and machine learning provided by the present invention includes the following steps in S1: S101. Create a periodic NURBS curve: Select a p-order NURBS curve; set a uniform node vector; set n independent control points and distribute the n control points equally in a circle in a two-dimensional plane, with the first control point coinciding with the last control point; independently set the weight value of each control point and constrain the weight value of each control point between 0 and 1; where p is the order of the NURBS curve and > 1; Specifically, in this step S101, the order p of the NURBS curve is preferably 3rd. Since 3rd order results in a smoother curve (C... 2A good balance can be achieved between continuity and computational complexity; therefore, in this invention, the order p of the NURBS curve is preferably 3. Of course, the order p of the NURBS curve can be 2 or higher (e.g., 4, 5, etc.), but not as optimal as 3. Furthermore, it should be noted that in practical applications, the distribution of control points is not limited to a circular equidistant distribution; other symmetrical distributions (e.g., elliptical) or asymmetrical distributions can also be used. However, since a circular distribution combined with symmetrical constraints is an effective strategy for enhancing performance in the target direction (e.g., the Y-axis) while suppressing lateral (XZ plane) anisotropy, and other distribution forms increase optimization complexity or may introduce unnecessary anisotropy, in this invention, a circular equidistant distribution of control points is preferred.

[0028] S102. Constructing the Column Cross-Section: First, set m cross-section positions along the 1 / 2 axis of the column. At each cross-section position, apply the periodic NURBS curve created in S101 to generate a periodic closed cross-section profile. The periodic closed cross-section profile generated at each cross-section position is the cross-section profile shape of the column at that position. Then, using the mirror mapping principle, generate multiple periodic closed cross-section profiles set along the other 1 / 2 axis of the column, thus obtaining a complete cluster of cross-sections distributed along the column's axis. (See reference...) Figure 3 As shown; where m > 1; Specifically, in step S102, to meet the requirement of uniform stress distribution within the lattice material, an axial symmetry design criterion is preferred (function: simplifies design variables, ensures the geometric symmetry of the support column, and facilitates the uniformity of subsequent mechanical properties). This means defining section parameters only in a portion of the support column's axial length (e.g., a unilateral symmetric region), and generating a complete section cluster through mirror mapping. It should be noted that in practical applications, other symmetry methods (e.g., four-quadrant symmetry) or directly defining a complete section can also be considered, but these would increase the number of design variables. Therefore, in this invention, an axial symmetry (i.e., mirror symmetry) method is preferred for generating the complete section cluster.

[0029] S103, 3D Reconstructed Column: In computer-aided design software, the lofting function is used to connect the complete cross-section clusters distributed along the column axis obtained in S102, and reconstruct a single 3D column entity with a smooth transition variable cross-section. Specifically, in step S103, it is preferable to use the loft function in finite element analysis software (such as Abaqus) to connect the cross-sections distributed along the axial direction, reconstructing a single three-dimensional support solid with a smooth transition variable cross-section. (See [reference needed]) Figure 3 As shown.

[0030] S104. Construct a complete lattice structure: First, position the single three-dimensional support entity generated in S101 to the corresponding position of the lattice structure through rigid body transformation (such as translation and rotation). Then, generate a standard spatial array structure through rotation array and mirror transformation operations. Finally, perform a topology merging operation to form a complete lattice structure with periodic variable cross-section supports.

[0031] Specifically, the lattice structure optimization design method based on NURBS curves and machine learning provided by this invention includes the following steps in step S2: S201. Using the single lattice structure generated in S1 as a representative volume element (i.e., RVE), periodic boundary conditions are applied to it in the finite element analysis software. The boundary nodes of the representative volume element are bound to the reference node degrees of freedom through constraint equations to simulate the periodic repetition characteristics of the lattice structure in space and analyze the mechanical response of the complete lattice material. The expression of the constraint equations is as follows: The constraint equations described above define how the boundary of the representative volume element (RVE) should deform. They require that any pair of periodically corresponding points on the RVE (i.e., separated by a periodic vector) The difference between the field variables at the two points must be equal to the difference between the macroscopic average gradient and the periodic vector. The product of; where, These are the microscopic field variables that need to be solved; in mechanical analysis, they represent the displacement field. In thermal analysis, it represents the temperature field. ; It refers to the coordinates of a specific point inside the RVE. In the above formula, it represents the coordinates of a node on the boundary of the RVE. Represents the 𝛼th periodic vector (also called the span vector), and its geometric meaning is: pointing from one boundary surface of the RVE to the corresponding boundary surface on its opposite side; The physical meaning is microscopic field variables. The macroscopic far-field gradient (or volume-averaged gradient) is the core of the entire formula, a key quantity connecting the microscopic and macroscopic worlds. Angle brackets < > denote volume averaging, which is the average of the integral over the entire RVE volume. ,therefore, It is not a spatially varying micro-gradient, but a constant representing the overall macroscopic behavior of RVE. Furthermore, in the variables mentioned above, the subscript 𝑗 represents the coordinate component index, indicating the spatial dimension (x, y, z), where 𝑗 = 1, 2, 3 in three-dimensional space. 𝛼 represents the periodic vector index, used to indicate the periodic direction; each 𝛼 value corresponds to a complete periodic vector.

[0032] S202. Under the set macroscopic strain drive (such as uniaxial strain in the Y direction), the equivalent elastic tensor of the representative volume element (i.e., RVE) is calculated using the volume averaging algorithm, and the equivalent Young's modulus in the target direction (such as the Y direction) is extracted.

[0033] Specifically, in this invention, step S2 serves to ensure accurate prediction of the macroscopic equivalent elastic properties (especially the equivalent Young's modulus) of the entire periodic lattice structure on a smaller RVE model by applying periodic boundary conditions to the representative volume element (RVE). This significantly reduces the computational cost of large-scale structural simulation and provides crucial support for efficient generation of training data and performance verification. Homogenization establishes a direct link between the geometric parameters of the micro-cell (i.e., RVE) and the macroscopic equivalent properties.

[0034] Specifically, the lattice structure optimization design method based on NURBS curves and machine learning provided by this invention uses a multilayer perceptron (MLP) neural network surrogate model constructed in S2. The input parameters of this neural network surrogate model are the geometric design parameters of the support column, namely the radius of the control point distribution circle of all independent sections of the support column. and independent weighting factors The output parameter is the equivalent Young's modulus of a representative volume element. and volume .

[0035] Specifically, the lattice structure optimization design method based on NURBS curves and machine learning provided by this invention adopts a double hidden layer structure in the neural network proxy model of the equivalent Young's modulus of the lattice structure and the neural network proxy model of the volume of the lattice structure in S2.

[0036] Specifically, the lattice structure optimization design method based on NURBS curves and machine learning provided by this invention uses the backpropagation (BP) algorithm to train the neural network surrogate model (including the neural network surrogate model of the equivalent Young's modulus of the lattice structure and the neural network surrogate model of the volume of the lattice structure) in S2.

[0037] Specifically, the lattice structure optimization design method based on NURBS curves and machine learning provided by this invention includes the following steps in S3 for training the neural network surrogate model (including the neural network surrogate model of the equivalent Young's modulus of the lattice structure and the neural network surrogate model of the lattice structure volume): S301. Data Generation: First, a large number of sample points are uniformly generated in the high-dimensional design parameter space using the Latin Hypercube Sampling (LHS) method, where the parameter space range is... , Then, for each sample point, parametric modeling is first performed using method S1, and then periodic boundary conditions and homogenization analysis are applied using method S2 to calculate its corresponding equivalent Young's modulus and volume, forming a structured dataset. S302, Model Training: First, the structured dataset generated in S301 is divided into a training set, a validation set, and a test set, with the training set accounting for 80%, the validation set accounting for 10%, and the test set accounting for 10%. Then, the training set is substituted into the neural network surrogate model (including the neural network surrogate model of the equivalent Young's modulus of the lattice structure and the neural network surrogate model of the volume of the lattice structure), and the backpropagation algorithm is used to train the neural network surrogate model (including the neural network surrogate model of the equivalent Young's modulus of the lattice structure and the neural network surrogate model of the volume of the lattice structure).

[0038] Specifically, the lattice structure optimization design method based on NURBS curves and machine learning provided by this invention aims to train the neural network surrogate model constructed in S3 (including the neural network surrogate model of the equivalent Young's modulus of the lattice structure and the neural network surrogate model of the lattice structure volume) to achieve high prediction accuracy (e.g., R) on independent test sets. 2 >0.99).

[0039] Specifically, the lattice structure optimization design method based on NURBS curves and machine learning provided by this invention includes the following steps in step S4: S401. Establish the equivalent Young's modulus in the target direction to maximize the target direction. and minimize volume Or equivalently minimize relative density The mathematical formulation of the multi-objective optimization problem with objective T is as follows: in, The radius of the circle used to distribute control points; The weighting factor for the control points; Equivalent Young's modulus; For volume; Number of cross sections; Number of control points; S402. A multi-objective genetic algorithm is used to solve the multi-objective optimization problem established in S402, and the Pareto optimal solution set is output. This optimal solution set is the optimal design scheme of the representative volume element (RVE) in S2.

[0040] Specifically, in step S4, for the multi-objective optimization problem, the multi-objective genetic algorithm adopted can be the NSGA-II (Non-dominated Sorting Genetic Algorithm II) multi-objective genetic algorithm, or other advanced multi-objective evolutionary algorithms (such as MOEA / D) or multi-objective particle swarm optimization (MOPSO). More specifically, when the NSGA-II multi-objective genetic algorithm is used to solve the multi-objective optimization problem, the algorithm parameters need to be set first, such as the population size (e.g., N=800), the optimal individual coefficient (e.g., 0.35), the maximum number of generations (e.g., 300), and the early termination condition (e.g., no significant improvement in the Pareto front hypervolume for 50 consecutive generations); during the optimization iteration process, for the objective function value ( , The evaluation is rapidly provided by the neural network surrogate model trained in S3, replacing the traditional, computationally expensive finite element analysis. After the multi-objective genetic algorithm runs, the output Pareto optimal solution set (Pareto Front) represents the representative volume element (RVE) in S2. and (or The optimal design scheme under different trade-offs between )

[0041] Furthermore, it should be noted that the optimization objective can be adjusted according to actual needs, except... and (or In addition to the above, other targets (such as shear modulus, buckling strength, energy absorption efficiency) or constraints (such as manufacturing constraints) can be introduced according to specific application requirements.

[0042] To further understand how the NURBS curve and machine learning-based lattice structure optimization design method provided by this invention is implemented and what effects it achieves, the following explanation uses a BCC lattice structure as an example: Step 1: Create a periodic NURBS curve 1. Parameter settings Independent design sections: 3; Independent control points: 8, evenly distributed along a distribution circle with a radius of 0.5 < <3.0; Weight factor: Set the weight value for each control point independently, with a constraint range of 0 < ≤1; Node vectors: Using uniform node vectors, cubic periodic closed NURBS curves are generated. (See reference...) Figure 2 As shown; 2. Curve generation By using an Abaqus / CAE secondary development script (Python language) to call the spline method, inputting the coordinates of control points and weight factors, a spline function that satisfies C... 2 A continuous curve; Step 2: BCC lattice structure modeling 1. Construction of BCC lattice structure support section Three equally spaced independent section positions are set along the 1 / 2 axis of the BCC lattice structure support; At each cross-sectional location, a periodic closed cross-sectional profile is generated by applying the periodic NURBS curve created in the first step. Then, two more periodic closed cross-sectional profiles are generated along the other half of the support axis using the mirror mapping principle, resulting in a complete cluster of cross-sections distributed along the support axis. (See [reference]). Figure 3 As shown; 2. Generation of BCC lattice structure In Abaqus, use the loft function to connect the sections and generate a single variable cross-section support (10 mm in length). The generated single variable cross-section pillars are positioned at standard node positions of the BCC lattice through rigid body transformations such as translation and rotation. Then, through geometric transformations such as rotation array and mirroring, a standard spatial array structure of the BCC lattice is generated. Finally, a topological merging operation is performed to form a complete BCC lattice cell with periodic variable cross-section pillars, i.e., a BCC lattice structure. (See [reference]) Figure 4 As shown; Step 3: Training and Optimization of the Agent Model 1. Data Collection Geometric parameters: 4000 parameter combinations were generated using Latin hypercube sampling (LHS). ; Mechanical properties: Apply periodic boundary conditions (PBCs) to each parameter combination in Abaqus and calculate the equivalent Young's modulus in the Y direction. and volume This forms a structured dataset; Mesh settings: A uniform C3D4 tetrahedral mesh with a seed size of 0.508 mm is used (sensitivity verified). 2. Neural Network Modeling Architecture: The surrogate model is a 17-16 neuron double-hidden-layer MLP; The surrogate model is a 15-9 neuron double-hidden-layer MLP; Training: 80% training data, 10% validation data, 10% testing data, optimized R. 2 >0.99.

[0043] 3. Multi-objective optimization Objective function: Maximize , minimize ; Algorithm: NSGA-II multi-objective genetic algorithm; Algorithm parameters: population size 800, optimal individual coefficient 0.35, maximum number of generations 300. Output: Pareto front solution set, from which select solutions with relative densities ρ≈0.20, 0.30, and 0.40 (V≈307.9mm). 3 461.9 mm 3 615.8 mm 3 ), see Figures 5 to 8 ; Step 4: Sample Preparation and Verification 1. Additive Manufacturing Equipment: Laser Powder Bed Fusion (LPBF, Uniwin Technology GT100).

[0044] Material: Ti-6Al-4V titanium alloy (elastic modulus 104 GPa, Poisson's ratio 0.35).

[0045] Process parameters: laser power 60 W, scanning speed 1700 mm / s, layer thickness 20 μm, argon protection.

[0046] 2. Post-processing Sandblasting: 180μm Al2O3 abrasive is used to remove residual powder.

[0047] Annealing: Hold at 800℃ for 2 hours, then furnace cool to 200℃ to eliminate residual stress.

[0048] 3. Performance Testing: Compression test: MTS E45.305 testing machine, loading rate 3.0 mm / min.

[0049] Results: The N-BCC structure showed a 18.1%–144.8% increase in modulus compared to the traditional BCC structure. (See reference...) Figure 9 As shown.

[0050] Figure 2 The diagram shown is a schematic representation of the parameters of a 3-period NURBS curve; in Figure 2 In this context, P0, P1, P2, ..., P8 represent control points; W0, W1, W2, ..., W8 represent control point weight factors; u3, u4, ..., u 10 R1, R2, and R3 represent the node vectors; R1, R2, and R3 represent the radii of the control point distribution circle.

[0051] Figure 3 The diagram shown illustrates the construction process of the BCC lattice structure support cross-section. Figure 3 The numbers = 1 GB3 MERGEFORMAT ①, = 2 GB3 MERGEFORMAT ②, and = 3 GB3 MERGEFORMAT ③ represent the cross-section of the support column.

[0052] Figure 4 The diagram shown illustrates the generation process of the BCC lattice structure.

[0053] Figure 5 The diagram shown illustrates the optimization process of the BCC lattice structure.

[0054] Figure 6 The figures show the stress-strain curves of the BCC lattice structure generated by the conventional method and the BCC lattice structure sample generated by the method of this invention when ρ=0.211.

[0055] Figure 7 The figures show the stress-strain curves of the BCC lattice structure generated by the conventional method and the BCC lattice structure sample generated by the method of this invention when ρ=0.300.

[0056] Figure 8 The figures show the stress-strain curves of the BCC lattice structure generated by the conventional method when ρ=0.402 and the BCC lattice structure sample generated by the method of the present invention after optimization.

[0057] Figure 9 The comparison shows the elastic modulus of a BCC lattice structure generated by a conventional method and a BCC lattice structure sample generated by the method of the present invention.

[0058] It should be noted that, in Figures 6 to 9 In the text, BCC represents the BCC lattice structure sample generated by the conventional method; N-BCC represents the BCC lattice structure sample generated after optimization using the method of this invention.

[0059] As can be seen from the above, the lattice structure optimization design method based on NURBS curves and machine learning provided by this invention has achieved significant breakthroughs in technical performance, computational efficiency, manufacturing applicability, and economic benefits compared to traditional lattice structure optimization design methods, as detailed below: 1. Technical performance Significantly enhanced mechanical properties: The BCC lattice structure optimized by the method of this invention has a significantly improved equivalent Young's modulus in the Y direction compared with the traditional BCC lattice structure at the same relative density. Especially at low relative density (ρ=0.211), the modulus is improved by up to 144.8%, breaking through the performance limit of lightweight structures.

[0060] 2. Computational efficiency By employing an MLP neural network surrogate model (with a dual hidden layer structure) to replace traditional finite element analysis, the time required for a single performance prediction is reduced from minutes to seconds; the model's prediction accuracy for equivalent Young's modulus and volume reaches R0. 2 >0.996, which meets the requirements for engineering optimization.

[0061] 3. Manufacturing applicability Parametric design supports customization: By adjusting the control point distribution radius and weight factor, the cross-sectional shape of the support column (such as prismatic protrusions and tapered gradients) can be flexibly adjusted to adapt to different mechanical scenario requirements (such as energy absorption and impact resistance).

[0062] 4. Economic benefits Lightweight and material savings: Under the same modulus requirements, the relative density of the lattice structure is lower, which directly reduces the amount of high-cost materials (such as Ti-6Al-4V) used.

[0063] Finally, it should be noted that the above description is only an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for optimizing the design of lattice structures based on NURBS curves and machine learning, characterized in that, Includes the following steps: S1. Parametric modeling of lattice structures based on periodic NURBS curves: Generating lattice structures with periodic variable cross-section supports using periodic NURBS curves. S2. Apply periodic boundary conditions and homogenization: Using the lattice structure generated in S1 as a representative volume element, apply periodic boundary conditions and homogenization analysis to it, and calculate its equivalent Young's modulus and volume. S3. Construction and training of neural network surrogate models: A multilayer perceptron neural network model is established as a surrogate model for the equivalent Young's modulus and volume of the lattice structure in S2, and the constructed neural network surrogate model is trained; the neural network surrogate model includes a neural network surrogate model for the equivalent Young's modulus of the lattice structure and a neural network surrogate model for the volume of the lattice structure. S4. Structural parameter optimization based on multi-objective genetic algorithm: Establish a multi-objective optimization problem with the objectives of maximizing the equivalent Young's modulus in the target direction and minimizing the volume or equivalently minimizing the relative density. Solve the problem using a multi-objective genetic algorithm and output the Pareto optimal solution set. The Pareto optimal solution set is the optimal design scheme of the representative volume unit in S2.

2. The lattice structure optimization design method based on NURBS curves and machine learning according to claim 1, characterized in that, S1 specifically includes: S101. Create a periodic NURBS curve: Select a p-order NURBS curve; set a uniform node vector; set n independent control points and distribute the n control points equally in a circle in a two-dimensional plane, with the first control point coinciding with the last control point; independently set the weight value of each control point and constrain the weight value of each control point to between 0 and 1; where p is the order of the NURBS curve and > 1; S102. Constructing the column cross-section: First, set m cross-section positions along the 1 / 2 axis of the column, and apply the periodic NURBS curve created in S101 to each cross-section position to generate a periodic closed cross-section profile. The periodic closed cross-section profile generated at each cross-section position is the cross-section profile shape of the column at that cross-section position. Then, generate multiple periodic closed cross-section profiles along the other 1 / 2 axis of the column through the mirror mapping principle, thereby obtaining a complete cross-section cluster distributed along the axis of the column; where m > 1. S103, 3D Reconstructed Column: In computer-aided design software, the lofting function is used to connect the complete cross-section clusters distributed along the column axis obtained in S102, and reconstruct a single 3D column entity with a smooth transition variable cross-section. S104. Construct a complete lattice structure: First, position the single three-dimensional support entity generated in S101 to the corresponding position of the lattice structure through rigid body transformation. Then, generate a standard spatial array structure through rotation array and mirror transformation operations. Finally, perform a topology merging operation to form a complete lattice structure with periodic variable cross-section supports.

3. The lattice structure optimization design method based on NURBS curves and machine learning according to claim 1, characterized in that, S2 specifically includes: S201. Using the single lattice structure generated in S1 as a representative volume element, periodic boundary conditions are applied to it in the finite element analysis software. The boundary nodes of the representative volume element are bound to the reference node degrees of freedom through constraint equations to simulate the periodic repetition characteristics of the lattice structure in space and analyze the mechanical response of the complete lattice material. The expression of the constraint equations is as follows: in, The microscopic field variables that need to be solved, These are the coordinates of a node on the boundary of a representative volume element. It is the ❛�th periodic vector. Microscopic field variables The macroscopic far-field gradient; S202. Under the set macroscopic strain drive, the equivalent elastic tensor of the representative volume element is calculated using the volume averaging algorithm, and the equivalent Young's modulus in the target direction is extracted.

4. The lattice structure optimization design method based on NURBS curves and machine learning according to claim 1, characterized in that, The neural network surrogate model constructed in S3 is a multilayer perceptron neural network model, whose input parameters are the geometric design parameters of the support column, namely the radius of the control point distribution circle for all independent sections of the support column. and independent weighting factors The output parameter is the equivalent Young's modulus of a representative volume element. and volume .

5. The lattice structure optimization design method based on NURBS curves and machine learning according to claim 1, characterized in that, The neural network proxy model for the equivalent Young's modulus of the lattice structure and the neural network proxy model for the volume of the lattice structure both adopt a double hidden layer structure.

6. The lattice structure optimization design method based on NURBS curves and machine learning according to claim 1, characterized in that, In S3, the training of the neural network surrogate model specifically employs the backpropagation algorithm.

7. The lattice structure optimization design method based on NURBS curves and machine learning according to claim 6, characterized in that, The specific steps for training the neural network surrogate model in S3 are as follows: S301. Data Generation: First, a large number of sample points are uniformly generated in the high-dimensional design parameter space using the Latin hypercube sampling method, where the parameter space range is... , Then, for each sample point, parametric modeling is first performed using method S1, and then periodic boundary conditions and homogenization analysis are applied using method S2 to calculate its corresponding equivalent Young's modulus and volume, forming a structured dataset. S302, Model Training: First, the structured dataset generated in S301 is divided into a training set, a validation set, and a test set, with the training set accounting for 80%, the validation set accounting for 10%, and the test set accounting for 10%. Then, the training set is substituted into the neural network proxy model, and the neural network proxy model is trained using the error backpropagation algorithm.

8. The lattice structure optimization design method based on NURBS curves and machine learning according to claim 1, characterized in that, S4 specifically includes: S401. Establish the equivalent Young's modulus in the target direction to maximize the target direction. and minimize volume Or equivalently minimize relative density The mathematical formulation of the multi-objective optimization problem with objective T is as follows: in, The radius of the circle used to distribute control points; The weighting factor for the control points; Equivalent Young's modulus; For volume; Number of cross sections; Number of control points; S402. A multi-objective genetic algorithm is used to solve the multi-objective optimization problem established in S402, and the Pareto optimal solution set is output. The optimal solution set is the optimal design scheme of the representative volume unit in S2.

Images