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

Abstract

The invention discloses a 3D printing topological optimization method and system based on RBF mapping and a genetic algorithm, and the method comprises the steps: carrying out the angle initialization of each individual through employing a hybrid strategy, and carrying out the density initialization of a synchronous constraint density interval; differentiated mapping is carried out on each individual based on a three-dimensional radial basis function, and low-dimensional global control points are mapped into a local angle field and a density field; performing local optimization by using finite element analysis and sensitivity filtering, and jointly updating the angle and the density; performing global optimization based on a genetic algorithm and local feedback; iteration is carried out after population recombination, iteration is finished until target function convergence judgment and maximum iteration number limitation are met, and an optimal solution is output. The method has the advantages that the genetic algorithm (GA) and the radial basis function (RBF) interpolation model are combined, the influence of anisotropy is considered, the transverse isotropic model is used, and compared with an existing method, the calculation time is remarkably shortened, and the optimization effect is remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of 3D printing continuous fiber composite material topology optimization design, and particularly relates to a 3D printing topology optimization method and system based on RBF mapping and genetic algorithm. BACKGROUND

[0002] Additive manufacturing technology, i.e. 3D printing technology, is a technology that uses wire or metal powder as raw material, loads a slice model, and realizes three-dimensional structure forming through layer-by-layer accumulation, and has the advantages of strong flexibility, high material utilization rate, and insensitivity to structural complexity, and can realize personalized customization and rapid prototyping of complex structures.

[0003] Continuous fiber reinforced composite material is a high-performance composite material formed by combining high-strength fibers (such as glass, carbon, and boron fibers) with matrix materials (such as plastics, resins, rubbers, and metals), and has the advantages of high specific strength and specific modulus, corrosion resistance, and strong designability, and is an ideal substitute material for traditional metal materials. For 3D printing of continuous fiber reinforced composite materials, the main method is based on extrusion molding layer-by-layer stacking technology, which impregnates continuous fibers and matrix materials (such as thermoplastic resins) and then lays them layer by layer to realize free laying of fiber paths and deposition forming of parts, which can maximize the reinforcing performance of fibers.

[0004] Topology optimization is a method of optimizing material distribution in a given area according to given load conditions, constraint conditions, and performance indicators.

[0005] In the current existing topology optimization method, the topology optimization is usually based on the isotropic model, and most of them do not consider that the actual situation rarely has isotropic materials. At the same time, when performing topology optimization on a component, the simultaneous optimization of density and angle needs to be considered, but the simultaneous optimization of density and angle for each unit will make the calculation process very complex and require a lot of time.

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

[0007] In view of the deficiencies of the prior art, the present application aims to provide a 3D printing topology optimization method and system based on RBF mapping and genetic algorithm, which can rationalize the topology optimization results and improve efficiency.

[0008] To achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows:

[0009] The application provides a 3D printing topology optimization method based on RBF mapping and a genetic algorithm.

[0010] Step 1: angle initialization is performed on each individual by using a hybrid strategy, and density initialization is performed by synchronously limiting the density interval;

[0011] Step 2: each individual is differentially mapped based on a three-dimensional radial basis function, and low-dimensional global control points are mapped into a local angle field and a density field;

[0012] Step 3: local optimization is performed by using finite element analysis and sensitivity filtering, and angles and densities are jointly updated;

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

[0014] Step 5: population recombination is performed, and the process returns to step 2 for iteration until a target function convergence judgment is met and a maximum iteration number limit is reached, and then the iteration is ended, and an optimal solution is output.

[0015] Further, the specific process of angle initialization performed on each individual by using a hybrid strategy in step 1 comprises the following steps.

[0016] An individual is created, and a fixed number of global control points are contained in each individual;

[0017] Angle initialization: a hybrid strategy is used to set the selection probability of the angle, 30% of the probability is used to select a fixed angle, and 70% of the probability is used to select a random angle; wherein the fixed angle is selected from the range of [0, 90°], and the random angle is selected from the range of [0, 180°].

[0018] Further, the density initialization in step 1 is performed by using a density generation formula to initialize the density, and the density is uniformly distributed in the interval of [0.1, 0.9], and the density generation formula is as follows:

[0019] ρ init = 0.1 + 0.8 * rand(1)

[0020] Wherein, rand(1) ∈ [0, 1].

[0021] Further, the specific process of differentially mapping each individual based on a three-dimensional radial basis function in step 2 comprises the following steps.

[0022] Step 2.1: the global control point grid is uniformly divided according to the size of the three-dimensional design space to be optimized, and a fixed number of effective control points are intercepted;

[0023] Step 2.2: the distance weight of each local unit and the effective control point is calculated by using a Gaussian radial basis function.

[0024] Step 2.3, normalizing the RBF value and weighted interpolation to calculate the local field parameter, diffusing the parameter of the global control point to the local unit through the weight to obtain the continuous angle field and density field;

[0025] Step 2.4, performing the range constraint processing of the angle and the physical boundary truncation of the density.

[0026] Further, the calculation method of the weighted interpolation to calculate the local field parameter in step 2.3 is as follows:

[0027] The angle calculation formula of the local unit is:

[0028]

[0029] The density calculation formula of the local unit is:

[0030]

[0031] Wherein, θ j is the angle value of the effective control point j, ρ j is the density value of the effective control point j, is the normalized RBF value, is the RBF value, d i is the Euclidean distance between each local unit and the effective control point, and σ is the shape parameter.

[0032] Further, the specific way of jointly updating the angle and the density in step 3 is as follows:

[0033] Updating the density based on the moving asymptote method;

[0034] Updating the angle based on the angle gradient descent method;

[0035] The density update step and the angle update step are both adjusted by using dynamic parameters.

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

[0037] Step 4.1, roulette wheel selection of individuals;

[0038] Step 4.2, two-point crossover, and the crossover point is preferentially selected at the boundary between the global control point groups to reserve complete spatial segments;

[0039] Step 4.3, mutation operation is performed on the global control point, in which the angle mutation adopts additive mutation to ensure the continuity of the physical direction, and the density mutation adopts multiplicative mutation to conform to the nonlinearity of the density.

[0040] In a second aspect, the present application provides a 3D printing topology optimization method for implementing the method of the first aspect, and the key lies in comprising:

[0041] An initialization module is configured to perform angle initialization on each individual by using a hybrid strategy and to perform density initialization on a constraint density interval in a synchronous manner;

[0042] A differential mapping module is configured to perform differential mapping on each individual by using a three-dimensional radial basis function, and to map a low-dimensional global control point to a local angle field and a density field;

[0043] A local optimization module is configured to perform local optimization by using finite element analysis and sensitivity filtering, and to update angles and densities in a combined manner;

[0044] A global optimization module is configured to perform global optimization based on a genetic algorithm and local feedback;

[0045] A judgment module is configured to judge whether an iteration end condition is met, and if yes, output an optimal solution, and if not, repeat iteration after population recombination.

[0046] In a third aspect, the present application provides a computer device, which comprises a processor, a memory, and a computer program stored on the memory and capable of running on the processor, and the computer program is executed by the processor to implement the steps of the method of the first aspect.

[0047] In a fourth aspect, the present application provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the steps of the method of the first aspect.

[0048] The present application has the following remarkable effects: the present application combines a genetic algorithm (GA) and a radial basis function (RBF) interpolation model, uses an isotropic model considering anisotropy, and performs topology optimization on a 90x4x27 component to obtain a lower flexibility value; compared with a method of performing block processing by using a Voronoi diagram, the calculation time is reduced by 42%, and the optimization effect is obviously improved. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 The method flowchart of the first embodiment of the present application is shown in the figure;

[0050] Figure 2 The control point position diagram when x=0 in the present application is shown in the figure;

[0051] Figure 3 The optimization process diagram of the present application is shown in the figure;

[0052] Figure 4 The principle block diagram of the second embodiment of the present application is shown in the figure;

[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, differentially map each individual based on three-dimensional radial basis functions, map low-dimensional global control points to local angle field, density field;

[0066] In some embodiments, the specific process of differentially mapping each individual based on three-dimensional radial basis functions in this step includes:

[0067] Step 2.1, uniformly divide the global control point grid according to the size of the three-dimensional design space to be optimized, dynamically generate the minimum three-dimensional grid dimension according to the defined control point number n, and meet

[0068] dim 3 ≥n

[0069] Generate coordinate points along the x, y, and z directions, respectively, generate complete grid point coordinates in the entire design space, and directly intercept the first fixed number as effective control points. When x = 0, the control point position is as follows Figure 2 as shown.

[0070] Step 2.2, calculate the distance weight of each local unit and the effective control point through the Gaussian radial basis function (RBF);

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

[0072]

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

[0074]

[0075] Where σ is the shape parameter, and the control function decays at a rate.

[0076] Step 2.3, normalize the RBF value and calculate the local field parameter by weighted interpolation, diffuse the parameters of the global control points to the local unit through the weight, and obtain the continuous angle field and density field;

[0077] Normalize the RBF value:

[0078]

[0079] Then, the local field parameter is calculated by weighted interpolation, the parameters of the global control points are diffused to the local unit through the weight, and the continuous angle field and density field are obtained. The angle θ(X) of the local unit is weighted and summed by the angles of all control points:

[0080]

[0081] Similarly, the density of local element is ρ(X) = ρ0exp(αX).

[0082]

[0083] Step 2.4, range constraint is performed on the angle, which is limited in [0°, 180°], and physical boundary truncation is performed on the density, which is limited in [0.01, 0.99].

[0084] Step 3, local optimization is performed by using finite element analysis and sensitivity filtering, and the angle and the density are updated jointly; specifically, the density is updated based on the moving asymptote method (MMA); the angle is updated based on the angle gradient descent method; the update step of the density and the update step of the angle are both adjusted by using a dynamic parameter.

[0085] In this embodiment, the specific steps of updating the density based on the moving asymptote method (MMA) are as follows:

[0086] The original sensitivity of the compliance to the density is calculated by finite element analysis The sensitivity filtering is performed by using a neighborhood weighted average with a radius r min The volume constraint sensitivity is calculated and is filtered synchronously. When updating, a dynamic step control is introduced:

[0087] move = 0.2 × move_factor

[0088] wherein move_factor is a dynamic parameter, and the initial value is 0.8.

[0089] The Lagrange multiplier λ that satisfies the volume constraint is solved by using a dichotomy method, and the optimization criterion is updated:

[0090]

[0091] The boundary processing forces the density value to be located in the interval [0, 1], so as to prevent numerical overflow. The dynamic parameter move_factor is adjusted adaptively with iteration, a larger step is used in the initial stage to accelerate convergence, and a smaller step is used in the later stage to improve precision.

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

[0093] The original sensitivity of the compliance to the angle is calculated Then, the sensitivity magnitude is balanced by using an exponential transformation:

[0094]

[0095] The same radius sensitivity filtering is performed to ensure the angular field smoothness. The update step is set as:

[0096] move = 5° x move_factor

[0097] The update formula is constructed with the scaling factor 15:

[0098] θ new = θ - 15 · D k

[0099] The boundary constraint processing adopts a periodic correction: when θ new <0°, it is rolled back to θ + 5° x move_factor, when θ new >180°, it is rolled back to θ - 5° x move_factor, ensuring that the angle value is always in the interval [0°, 180°].

[0100] where the density and angle share the dynamic parameter move_factor to realize step coordination, providing a larger step at the beginning to quickly reduce the objective function, and gradually reducing the step to quickly reduce the objective function when converging.

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

[0102] In some embodiments, the specific steps of global optimization based on genetic algorithm and local feedback are as follows:

[0103] In the selection operation, the selection is performed in the way of combining elite preservation with roulette, and the top 10% of the optimal individuals of each generation are directly entered into the next generation, and the remaining 90% of the individuals are selected according to the fitness value, and the higher the fitness value, the greater the probability of being selected;

[0104] In the crossover operation, two crossover points are randomly selected, and the gene fragments of the parent individuals between the two points are exchanged, and after execution, the control point angle value is forced to be mapped in the range of [0°, 180°], the density value is truncated in the range of [0.01, 0.99], and the spatial coordinates of the control points are reordered to ensure topological continuity;

[0105] In the mutation operation, the control point angle is randomly adjusted in a Gaussian disturbance manner, with a disturbance range of ±30°, and the control point density is adjusted in a proportional mutation manner, with a variation amplitude of ±20%, and the mutation probability (Pm) is adaptively adjusted in the optimization process, being higher at the beginning to enhance exploration and being lower at the later stage to stabilize convergence.

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

[0107]

[0108] Wherein, a linearly decreases from 0.5 to 0.1; according to the local convergence speed dynamic adjustment of genetic parameters, when fast convergence (change amount δ < 0.001), the crossover rate is reduced by 10%, the mutation rate is reduced by 20%, when oscillation (δ > 0.01), the crossover rate is increased by 15%, the mutation rate is increased by 25%, when stagnation (continuous 3 generations δ < 0.0001), trigger P m = 0.3 of forced variation breaks through local optimum. Thus, by adjusting the fitness evaluation of the control point, the strength of mutation and crossover is dynamically adjusted by the convergence of local optimization, balancing exploration and development.

[0109] Step 5, after the selection, crossover and mutation of the population are completed, the new generation of control point parameters is input into the RBF interpolation module to generate updated angle field and density field, and the local optimization process is entered. Iteration continues until the relative change rate of the objective function (compliance value) is less than the threshold value and the maximum iteration number is reached, and the cycle is ended. The optimization process is compared with the method of GA + Thiessen polygon as Figure 3 shown.

[0110] Example 2:

[0111] As Figure 4 shown, this embodiment proposes a 3D printing topology optimization method for implementing the method described in embodiment 1, which is characterized by comprising:

[0112] An initialization module is used to initialize the angle of each individual using a mixed strategy, and to initialize the density of the synchronous constraint density interval;

[0113] A differential mapping module is used to map each individual using three-dimensional radial basis functions for differential mapping, mapping low-dimensional global control points to local angle field and density field;

[0114] A local optimization module is used to perform local optimization using finite element analysis and sensitivity filtering to update angles and densities jointly;

[0115] A global optimization module is used to perform global optimization based on genetic algorithm and local feedback;

[0116] A judgment module is used to judge whether the iteration end condition is met, if yes, output the optimal solution, otherwise repeat the iteration after population recombination.

[0117] Example 3:

[0118] As Figure 5As shown, the embodiment provides a computer device, comprising a processor, a memory, and a computer program stored on the memory and capable of running on the processor, the processor and the memory being connected through a communication interface, and the computer program, when executed by the processor, implements the steps of the method according to the embodiment 1.

[0119] Embodiment 4:

[0120] The embodiment provides a computer readable storage medium, and the computer readable storage medium stores a computer program, and the computer program, when executed by a processor, implements the steps of the method according to the embodiment 1.

[0121] In conclusion, the embodiment of the present application combines the genetic algorithm (GA) and the radial basis function (RBF) interpolation model, considers the influence of anisotropy using the transverse isotropic model, performs topology optimization on a 90*4*27 component, and obtains a smaller flexibility value; compared with the existing optimization method, the calculation time is significantly reduced, and the optimization effect is significantly improved.

[0122] The technical solutions provided by the present application are described in detail above. The principles and implementation modes of the present application are described by applying specific examples in this paper, and the above embodiment is only used to help understand the method of the present application and its core idea. It should be pointed out that for ordinary skilled persons in the technical field, some improvements and modifications can be made to the present application without departing from the principles of the present application, and these improvements and modifications also fall within the protection scope of the claims of the present application.

Claims

1. A 3D printing topology optimization method based on RBF mapping and genetic algorithm, characterized in that, Comprising the following steps: Step 1, adopt a mixed strategy for angle initialization for each individual, and simultaneously constrain the density interval for density initialization; Step 2, difference mapping for each individual based on three-dimensional radial basis function, mapping low-dimensional global control points to local angle field, density field; Step 3, local optimization using finite element analysis and sensitivity filtering, joint update angle and density; Step 4, global optimization based on genetic algorithm and local feedback; Step 5, population recombination, return to step 2 for iteration until the target function converges and the maximum iteration limit is met, and the optimal solution is output. 2.The RBF mapping and genetic algorithm based 3D printing topology optimization method according to claim 1, characterized in that: The specific process of the angle initialization for each individual in step 1 includes: Create individuals, each individual contains a fixed number of global control points; Initialize the angle: adopt a mixed strategy to set the selection probability of the angle, 30% probability to select a fixed angle, 70% probability to select 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 RBF mapping and genetic algorithm based 3D printing topology optimization method according to claim 2, characterized in that: The density initialization in step 1 is to initialize the density using a density generation formula and uniformly distribute it in the [0.1, 0.9] interval, the density generation formula is: p init = 0.1 + 0.8 x rand(1) Where rand(1) ∈ [0, 1]. 4.The RBF mapping and genetic algorithm based 3D printing topology optimization method according to claim 1, wherein: The specific process of difference mapping for each individual based on three-dimensional radial basis function in step 2 includes: Step 2.1, uniformly divide the global control point grid according to the size of the three-dimensional design space to be optimized, and intercept a fixed number of effective control points; Step 2.2, calculate the distance weight of each local unit and the effective control point through the Gaussian radial basis function; Step 2.3, normalize the RBF value and calculate the local field parameter by weighted interpolation, diffuse the global control point parameters to the local unit through the weight, and get the continuous angle field and density field; Step 2.4, range constraint processing for angle and physical boundary truncation for density.

5. The method of claim 4, wherein the method is based on RBF mapping and genetic algorithm for 3D printing topology optimization. The calculation method of weighted interpolation calculation of local field parameter in step 2.3 is as follows: The angle calculation formula of the local unit is: The density calculation formula of the local unit is: where θ j is the angle value of the effective control point j, ρ j is the density value of the effective control point j, is the normalized RBF value, is the RBF value, d i is the Euclidean distance between each local cell and the effective control point, and σ is the shape parameter. 6.The RBF mapping and genetic algorithm based 3D printing topology optimization method according to claim 1, wherein: The specific way of joint updating angle and density in step 3 is as follows: Update the density based on the moving asymptote method; Update the angle based on the angle gradient descent method; The density update step and the angle update step are adjusted by using dynamic parameters. 7.The RBF mapping and genetic algorithm based 3D printing topology optimization method according to claim 1, wherein: The specific process of global optimization based on genetic algorithm and local feedback in step 4 includes: Step 4.1, roulette selection of individuals; Step 4.2, two-point crossover, the crossover point is preferentially selected at the boundary between the global control point groups to retain complete space segments; Step 4.3, mutation operation on global control points, in the mutation operation, angle mutation adopts additive mutation to ensure the continuity of physical direction, and density mutation adopts multiplicative mutation to conform to the nonlinearity of density.

8. A 3D printing topology optimization system based on RBF mapping and genetic algorithm, for implementing the steps of the method of claims 1-7, characterized in that, Comprise: Initialization module, for angle initialization for each individual using a mixed strategy, and simultaneously constrain the density interval for density initialization; a differential mapping module configured to perform differential mapping on each individual using three-dimensional radial basis functions to map low-dimensional global control points to local angle fields and density fields; a local optimization module configured to perform local optimization using finite element analysis and sensitivity filtering to jointly update the angles and the densities; a global optimization module configured to perform global optimization based on a genetic algorithm and local feedback; a judging module configured to judge whether an iteration end condition is met, and if so, output an optimal solution, otherwise, repeat the iteration after population recombination.

9. A computer device, comprising: A computer program product comprising a processor, a memory, and a computer program stored on the memory and executable on the processor, the computer program, when executed by the processor, implementing the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: A computer program product comprising a processor, a memory, and a computer program stored on the memory and executable on the processor, the computer program, when executed by the processor, implementing the steps of the method according to any one of claims 1 to 7.

Images