A 3D printing topology optimization method based on RBF mapping and genetic algorithm

Abstract

The application discloses a kind of 3D printing topological optimization method and system based on RBF mapping and genetic algorithm, method includes the following steps: angle initialization is carried out to each individual using mixed strategy, and density initialization is carried out to synchronous constraint density interval;Each individual is mapped based on three-dimensional radial basis function, and low-dimensional global control point is mapped into local angle field, density field;Local optimization is carried out using finite element analysis and sensitivity filtering, and angle and density are updated jointly;Global optimization is carried out based on genetic algorithm and local feedback;After population recombination, iteration is carried out until meeting the target function convergence judgment and the maximum iteration number limit, and iteration ends, and the optimal solution is output.The significant effect is: combined with genetic algorithm (GA) and radial basis function (RBF) interpolation model, anisotropy is considered using transverse isotropic model, compared with existing method, calculation time is significantly reduced, and optimization effect is significantly improved.

Description

Technical Field

[0001] This invention relates to the field of topology optimization design technology for 3D printed continuous fiber composite materials, specifically to a 3D printing topology optimization method and system based on RBF mapping and genetic algorithm. Background Technology

[0002] Additive manufacturing technology, also known as 3D printing technology, uses filaments or metal powders as raw materials, loads sliced ​​models, and builds up three-dimensional structures layer by layer. It has advantages such as high flexibility, high material utilization, and insensitivity to structural complexity, and can realize personalized customization and rapid prototyping of complex structures.

[0003] Continuous fiber reinforced composites are high-performance composite materials formed by combining high-strength fibers (such as glass, carbon, and boron fibers) with matrix materials (plastics, resins, rubber, metals, etc.). They possess advantages such as high specific strength and specific modulus, corrosion resistance, and strong designability, making them ideal alternatives to traditional metallic materials. 3D printing of continuous fiber reinforced composites is primarily based on extrusion molding layer-by-layer stacking technology. Continuous fibers are impregnated with matrix materials (such as thermoplastic resins) and then laid layer by layer, allowing for free fiber path placement and component deposition, maximizing the reinforcing properties of the fibers.

[0004] Topology optimization is a method for optimizing the distribution of materials within a given region based on given load conditions, constraints, and performance indicators.

[0005] Current topology optimization methods are usually based on isotropic models, which often fail to consider that isotropic materials are rare in practice. Furthermore, when optimizing the topology of components, it is necessary to simultaneously optimize density and angle. However, the calculation process for simultaneously optimizing density and angle for each element is very complex and time-consuming.

[0006] Therefore, it is necessary to propose a method that considers non-isotropic materials and simplifies the calculation, in order to rationalize the topology optimization results and improve efficiency. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the purpose of this invention is to provide a 3D printing topology optimization method and system based on RBF mapping and genetic algorithms, which can rationalize the topology optimization results and improve efficiency.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] Firstly, this invention proposes a 3D printing topology optimization method based on RBF mapping and genetic algorithm, the key of which includes the following steps:

[0010] Step 1: Initialize the angle of each individual using a hybrid strategy, and simultaneously initialize the density within the constrained density range;

[0011] Step 2: Based on the three-dimensional radial basis function, perform differential mapping on each individual, and map the low-dimensional global control points into local angle fields and density fields;

[0012] Step 3: Perform local optimization using finite element analysis and sensitivity filtering, and jointly update the angle and density;

[0013] Step 4: Perform global optimization based on genetic algorithm and local feedback;

[0014] Step 5: Population recombination. Return to step 2 for iteration until the objective function convergence judgment and the maximum number of iterations are satisfied, then the iteration ends and the optimal solution is output.

[0015] Furthermore, the specific process of initializing the angle for each individual using a hybrid strategy, as described in step 1, includes:

[0016] Create individuals, each containing a fixed number of global control points;

[0017] Initialization angle: A hybrid strategy is used to set the angle selection probability, with a 30% probability of selecting a fixed angle and a 70% probability of selecting a random angle; wherein, the value range of the fixed angle is [0, 90°], and the value range of the random angle is [0, 180°].

[0018] Furthermore, the density initialization in step 1 involves initializing the density using a density generation formula and uniformly distributing it within the interval [0.1, 0.9]. The density generation formula is:

[0019] ρ init =0.1+0.8×rand(1)

[0020] Where rand(1)∈[0,1].

[0021] Furthermore, the specific process of performing differential mapping on each individual based on the three-dimensional radial basis function in step 2 includes:

[0022] Step 2.1: Divide the global control point grid evenly according to the required optimized 3D design space size, and extract a fixed number of effective control points;

[0023] Step 2.2: Calculate the distance weight between each local element and the effective control point using Gaussian radial basis functions;

[0024] Step 2.3: Normalize the RBF values ​​and calculate the local field parameters using weighted interpolation. Diffusion of the parameters of the global control points to the local elements is achieved through weighting, resulting in a continuous angle field and density field.

[0025] Step 2.4: Perform range constraint processing on the angle and physical boundary truncation of the density.

[0026] Furthermore, the calculation method for the weighted interpolation of local field parameters in step 2.3 is as follows:

[0027] The formula for calculating the angle of a local element is:

[0028]

[0029] The formula for calculating the density of local elements is:

[0030]

[0031] Where, θ j ρ is the angle value of the effective control point j. j To effectively control the density value at point j, The normalized RBF value. d is the RBF value. i Let σ be the Euclidean distance between each local element and the effective control point, and σ be the shape parameter.

[0032] Furthermore, the specific method for jointly updating the angle and density in step 3 is as follows:

[0033] Density is updated based on the moving asymptote method;

[0034] Angle updates based on angular gradient descent;

[0035] Both density update step size and angle update step size are adjusted using dynamic parameters.

[0036] Furthermore, the specific process of global optimization based on genetic algorithms and local feedback in step 4 includes:

[0037] Step 4.1: Select an individual using the roulette wheel;

[0038] Step 4.2: Perform two-point intersection. The intersection point should be selected at the boundary between global control point groups to preserve the complete spatial segment.

[0039] Step 4.3: Perform mutation operations on the global control points. In the mutation operation, the angle mutation adopts additive mutation to ensure the continuity of physical direction, and the density mutation adopts multiplicative mutation to conform to the density nonlinearity.

[0040] Secondly, the present invention proposes a 3D printing topology optimization method for implementing the method described in the first aspect, the key of which is:

[0041] The initialization module is used to initialize the angle of each individual using a hybrid strategy and to initialize the density of the constrained density range simultaneously.

[0042] The differential mapping module is used to perform differential mapping on each individual using three-dimensional radial basis functions, mapping low-dimensional global control points into local angle fields and density fields;

[0043] The local optimization module is used to perform local optimization using finite element analysis and sensitivity filtering, and to jointly update the angle and density.

[0044] The global optimization module is used for global optimization based on genetic algorithms and local feedback.

[0045] The judgment module is used to determine whether the iteration termination condition is met. If so, the optimal solution is output; otherwise, the iteration is repeated after population recombination.

[0046] Thirdly, the present invention provides a computer device including a processor, a memory, and a computer program stored in the memory and capable of running on the processor, wherein the computer program, when executed by the processor, implements the steps of the method described in the first aspect.

[0047] Fourthly, the present invention provides a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, implements the steps of the method as described in the first aspect.

[0048] The significant advantages of this invention are: it combines a genetic algorithm (GA) and a radial basis function (RBF) interpolation model, and uses a transverse isotropic model to consider the influence of anisotropy, and performs topology optimization on a 90×4×27 component, resulting in a lower compliance value; compared with the method of using Thiessen polygon diagram for block processing, the computation time is significantly reduced by 42%, and the optimization effect is significantly improved. Attached Figure Description

[0049] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention;

[0050] Figure 2 This is a diagram showing the control point positions when x = 0 in this invention;

[0051] Figure 3 This is a diagram illustrating the optimization process of the present invention;

[0052] Figure 4 This is a principle block diagram of Embodiment 2 of the present invention;

[0053] Figure 5 This is a principle block diagram of Embodiment 3 of the present invention. Detailed Implementation

[0054] The specific embodiments and working principles of the present invention will be further described in detail below with reference to the accompanying drawings.

[0055] Example 1:

[0056] like Figure 1 As shown in the figure, this embodiment proposes a 3D printing topology optimization method based on RBF mapping and genetic algorithm. The specific steps are as follows:

[0057] Step 1: Initialize the angle of each individual using a hybrid strategy, and simultaneously initialize the density within the constrained density range;

[0058] In some specific implementations, the specific steps for angle initialization using a hybrid strategy for each individual are as follows:

[0059] Create individuals, each containing a fixed number of global control points, that is, determine the number of global control points. Each control point (i.e. each individual) contains two design variables: angle and density.

[0060] Angle parameter initialization employs a hybrid strategy: a fixed angle set is defined as [0, 90°], and random angles range from [0, 180°]. A selection probability is set for the fixed angles: 30% probability of selecting a fixed angle (i.e., 30% probability of randomly selecting from the fixed angle set [0°, 90°]), and 70% probability of generating random angles (i.e., leveraging engineering experience to reinforce specific directions), with a 70% probability of uniformly and randomly generating angles within the range [0°, 180°] to ensure sufficient exploration of the design space.

[0061] The density initialization is performed by initializing the density using a density generation formula, and the density is uniformly distributed within the interval [0.1, 0.9]. The density generation formula is:

[0062] ρ init =0.1+0.8×rand(1)

[0063] Among them, rand(1)∈[0,1], rand(1) generates uniformly distributed random numbers in [0,1], ensuring that the density value is uniformly distributed in the interval [0.1,0.9], avoiding numerical problems caused by boundary values ​​0 and 1.

[0064] All parameters are subject to boundary constraints: the angle is strictly limited to the range of [0°, 180°], and the density is forcibly constrained to the interval of [0.01, 0.99] to prevent invalid solutions from being generated.

[0065] Step 2: Based on the three-dimensional radial basis function, perform differential mapping on each individual, and map the low-dimensional global control points into local angle fields and density fields;

[0066] In some implementations, the specific process of performing differential mapping on each individual based on three-dimensional radial basis functions as described in this step includes:

[0067] Step 2.1: Based on the required optimized 3D design space size, uniformly divide the global control point mesh. Dynamically generate the minimum 3D mesh dimension according to the defined number of control points n, satisfying...

[0068] dim 3 ≥n

[0069] Generate coordinate points along the x, y, and z directions for that dimension, generating a complete grid of point coordinates across the entire design space. Select a fixed number of these points as effective control points. The control point positions when x = 0 are as follows: Figure 2 As shown;

[0070] Step 2.2: Calculate the distance weight between each local element and the effective control point using Gaussian radial basis functions (RBF);

[0071] Let the coordinates of a local element be X = (x, y, z), and the global control point be C. i =(x i ,y i ,z i (i = 1, 2, ..., n), then the Euclidean distance between the local element and the control point is:

[0072]

[0073] Calculate the function value of the Gaussian RBF:

[0074]

[0075] Where σ is a shape parameter that controls the decay rate of the function.

[0076] Step 2.3: Normalize the RBF values ​​and calculate the local field parameters using weighted interpolation. Diffusion of the parameters of the global control points to the local elements is achieved through weighting, resulting in a continuous angle field and density field.

[0077] Normalize the RBF value:

[0078]

[0079] Next, weighted interpolation is used to calculate local field parameters. The parameters from the global control points are then diffused to the local elements using weights, resulting in continuous angle and density fields. The angle θ(X) of the local element is obtained by weighted summation of the angles from all control points.

[0080]

[0081] Similarly, the density ρ(X) of the local element is:

[0082]

[0083] Step 2.4: Constrain the angle to [0°, 180°] and physically truncate the density to [0.01, 0.99].

[0084] Step 3: Perform local optimization using finite element analysis and sensitivity filtering, and jointly update the angle and density; specifically, update the density based on the moving asymptotic method; update the angle based on the angular gradient descent method; both the density update step size and the angle update step size are adjusted using dynamic parameters.

[0085] In this embodiment, the specific steps for updating the density based on the Moving Asymptotic Method (MMA) are as follows:

[0086] The original sensitivity of compliance to density was calculated using finite element analysis. Using radius r min Sensitivity filtering is performed using a neighborhood-weighted average; volume constraint sensitivity is calculated. Synchronous filtering is also implemented. Dynamic step size control is introduced during updates:

[0087] move = 0.2 × move_factor

[0088] Here, move_factor is a dynamic parameter with an initial value of 0.8.

[0089] Solve for the Lagrange multipliers λ that satisfy the volume constraint using the bisection method, and then update the optimization criteria:

[0090]

[0091] Boundary handling forces density values ​​to reside in the [0,1] interval to prevent numerical overflow. The dynamic parameter move_factor is adaptively adjusted with iterations, with a larger step size initially accelerating convergence and a smaller step size later improving accuracy.

[0092] In this embodiment, the specific steps for updating the angle using the angular gradient descent method are as follows:

[0093] Calculate the original sensitivity of compliance to angle. Then, an exponential transformation is used to balance the sensitivity order of magnitude:

[0094]

[0095] Sensitivity filtering with the same radius ensures smoothness of the angle field. The update step size is set as follows:

[0096] move = 5° × move_factor

[0097] Construct the update formula by combining the scaling factor of 15:

[0098] θ new =θ-15·D k

[0099] Boundary constraint handling employs periodic correction: when θ new When <0°, regress to θ+5°×move_factor, when θ new When the angle is greater than 180°, it reverts to θ-5°×move_factor to ensure that the angle value is always within the range of [0°, 180°].

[0100] In this method, density and angle share the dynamic parameter move_factor to achieve step size coordination. Initially, a larger step size is provided to quickly reduce the objective function, and the step size is gradually reduced during convergence to quickly reduce the objective function.

[0101] Step 4: Perform global optimization based on genetic algorithm and local feedback;

[0102] In some implementations, the specific steps for global optimization based on genetic algorithms and local feedback are as follows:

[0103] In the selection process, a combination of elite retention and roulette wheel selection is used. The top 10% of the best individuals in each generation are directly selected for the next generation, while the remaining 90% of individuals are selected probabilistically based on their fitness values. The higher the fitness, the greater the probability of being selected.

[0104] In the crossover operation, two crossover points are randomly selected, and the gene segments of the parent individuals between these two points are exchanged. After execution, the angle values ​​of the control points are forced to be mapped to the range of [0°, 180°], and the density values ​​are truncated to the range of [0.01, 0.99]. The control points are then reordered according to their spatial coordinates to ensure topological continuity.

[0105] In the mutation operation, the angle of the control points is randomly adjusted by Gaussian perturbation with a perturbation range of ±30°. The density of the control points is adjusted by proportional mutation with a change range of ±20%. The mutation probability (Pm) is adaptively adjusted during the optimization process, with a higher probability in the early stage to enhance exploration and a lower probability in the later stage to stabilize convergence.

[0106] Finally, the density sensitivity and angle sensitivity generated by local optimization are aggregated into the average sensitivity of the control point region, which is fed back to the genetic algorithm and the fitness function is dynamically adjusted through an exponential weighting term.

[0107]

[0108] Specifically, α linearly decreases from 0.5 to 0.1; the genetic parameters are dynamically adjusted according to the local convergence speed. When convergence is rapid (change δ < 0.001), the crossover rate decreases by 10% and the mutation rate decreases by 20%. When oscillation occurs (δ > 0.01), the crossover rate increases by 15% and the mutation rate increases by 25%. When stagnation occurs (δ < 0.0001 for 3 consecutive generations), P is triggered. m A forced mutation of 0.3 breaks through local optima. By adjusting the fitness evaluation of control points, the intensity of mutation and crossover can be dynamically adjusted based on the convergence of local optimization, thus balancing exploration and exploitation.

[0109] Step 5: After completing the selection, crossover, and mutation operations of the population, the parameters of the new generation of control points are re-input into the RBF interpolation module to generate updated angle and density fields, and then the local optimization process begins. Iteration continues until the relative rate of change of the objective function (compliance value) is less than a threshold and the preset maximum number of iterations is reached, at which point the loop ends. The optimization process is compared to the GA+Thieson polygon method. Figure 3 As shown.

[0110] Example 2:

[0111] like Figure 4 As shown, this embodiment proposes a 3D printing topology optimization method for implementing the method described in Embodiment 1, the key of which includes:

[0112] The initialization module is used to initialize the angle of each individual using a hybrid strategy and to initialize the density of the constrained density range simultaneously.

[0113] The differential mapping module is used to perform differential mapping on each individual using three-dimensional radial basis functions, mapping low-dimensional global control points into local angle fields and density fields;

[0114] The local optimization module is used to perform local optimization using finite element analysis and sensitivity filtering, and to jointly update the angle and density.

[0115] The global optimization module is used for global optimization based on genetic algorithms and local feedback.

[0116] The judgment module is used to determine whether the iteration termination condition is met. If so, the optimal solution is output; otherwise, the iteration is repeated after population recombination.

[0117] Example 3:

[0118] like Figure 5As shown, this embodiment proposes a computer device, including a processor, a memory, and a computer program stored in the memory and capable of running on the processor. The processor and the memory are connected through a communication interface. When the computer program is executed by the processor, it implements the steps of the method described in Embodiment 1.

[0119] Example 4:

[0120] This embodiment proposes a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, it implements the steps of the method described in Embodiment 1.

[0121] In summary, this embodiment of the invention combines a genetic algorithm (GA) and a radial basis function (RBF) interpolation model, and uses a transverse isotropic model to consider the influence of anisotropy, to perform topology optimization on a 90×4×27 component, resulting in a smaller compliance value; compared with existing optimization methods, the computation time is significantly reduced and the optimization effect is significantly improved.

[0122] The technical solution provided by this invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. It should be noted that those skilled in the art can make several improvements and modifications to this invention without departing from the principles of this invention, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A 3D printing topology optimization method based on RBF mapping and genetic algorithm, characterized in that, Includes the following steps: Step 1: Initialize the angle of each individual using a hybrid strategy, and simultaneously initialize the density within the constrained density range; Step 2: Based on the three-dimensional radial basis function, perform differential mapping on each individual, and map the low-dimensional global control points into local angle fields and density fields; Step 3: Perform local optimization using finite element analysis and sensitivity filtering, and jointly update the angle and density; Step 4: Perform global optimization based on genetic algorithm and local feedback; Step 5: Population recombination. Return to step 2 for iteration until the objective function convergence judgment and the maximum number of iterations are satisfied, then the iteration ends and the optimal solution is output. The specific process of performing differential mapping on each individual based on the three-dimensional radial basis function in step 2 includes: Step 2.1: Divide the global control point grid evenly according to the required optimized 3D design space size, and extract a fixed number of effective control points; Step 2.2: Calculate the distance weight between each local element and the effective control point using Gaussian radial basis functions; Step 2.3: Normalize the RBF values ​​and calculate the local field parameters using weighted interpolation. Diffusion of the parameters of the global control points to the local elements is achieved through weighting, resulting in a continuous angle field and density field. Step 2.4: Perform range constraint processing on the angle and physical boundary truncation of the density; The calculation method for the weighted interpolation of local field parameters in step 2.3 is as follows: The formula for calculating the angle of a local element is: ； The formula for calculating the density of local elements is: ； in, Effective control point Angle value, Effective control point density value, The normalized RBF value. For RBF value, The Euclidean distance between each local element and the effective control point, For shape parameters; The specific method for jointly updating the angle and density in step 3 is as follows: Density is updated based on the moving asymptote method; Angle updates based on angular gradient descent; Both density update step size and angle update step size are adjusted using dynamic parameters.

2. The 3D printing topology optimization method based on RBF mapping and genetic algorithm according to claim 1, characterized in that: The specific process of initializing the angle for each individual using a hybrid strategy, as described in step 1, includes: Create individuals, each containing a fixed number of global control points; Initialization angle: A hybrid strategy is used to set the angle selection probability, with a 30% probability of selecting a fixed angle and a 70% probability of selecting a random angle; wherein, the value range of the fixed angle is [0, 90°], and the value range of the random angle is [0, 180°].

3. The 3D printing topology optimization method based on RBF mapping and genetic algorithm according to claim 2, characterized in that: The density initialization in step 1 involves initializing the density using a density generation formula and uniformly distributing it within the interval [0.1, 0.9]. The density generation formula is: ； in, .

4. The 3D printing topology optimization method based on RBF mapping and genetic algorithm according to claim 1, characterized in that: The specific process of global optimization based on genetic algorithms and local feedback in step 4 includes: Step 4.1: Select an individual using roulette; Step 4.2: Perform two-point intersection. The intersection point should be selected at the boundary between global control point groups to preserve the complete spatial segment. Step 4.3: Perform mutation operations on the global control points. In the mutation operation, the angle mutation adopts additive mutation to ensure the continuity of physical direction, and the density mutation adopts multiplicative mutation to conform to the density nonlinearity.

5. A 3D printing topology optimization system based on RBF mapping and genetic algorithm, used to implement the steps of the method according to any one of claims 1-4, characterized in that, include: The initialization module is used to initialize the angle of each individual using a hybrid strategy and to initialize the density of the constrained density range simultaneously. The differential mapping module is used to perform differential mapping on each individual using three-dimensional radial basis functions, mapping low-dimensional global control points into local angle fields and density fields; The local optimization module is used to perform local optimization using finite element analysis and sensitivity filtering, and to jointly update the angle and density. The global optimization module is used for global optimization based on genetic algorithms and local feedback. The judgment module is used to determine whether the iteration termination condition is met. If so, the optimal solution is output; otherwise, the iteration is repeated after population recombination.

6. A computer device, characterized in that: It includes a processor, a memory, and a computer program stored in the memory and capable of running on the processor, wherein the computer program, when executed by the processor, implements the steps of the method as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that: A computer program is stored on the computer-readable storage medium, which, when executed by a processor, implements the steps of the method as described in any one of claims 1 to 4.

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