A generative design method for 3D printing lattices with programmable vibration modes

Abstract

The present invention discloses a 3D printing lattice generative design method with programmable vibration modes, the method comprising: establishing a unit cell database according to different unit cell structures; obtaining the fundamental frequencies of different unit cell structures by using the fundamental frequency theoretical model of the lattice cell, constructing a unit cell structure-fundamental frequency data set, and using it for the training of the structure-fundamental frequency reverse design model; simulating high-order frequencies by using dynamic finite element analysis simulation software, constructing a unit cell structure-high-order frequency data set, and using it for the training of the structure-high-order frequency reasoning model; generating multiple groups of unit cell structures with specified fundamental frequencies by using the trained structure-fundamental frequency reverse design model; obtaining multiple orders of high-order frequencies of multiple groups of unit cell structures by using the trained structure-high-order frequency reasoning model; screening multiple groups of unit cell structures in turn by order according to the specified high-order frequencies, and obtaining a group of unit cell structures that meet the vibration mode requirements. The present invention realizes the generative design of the vibration mode of the unit cell.

Description

Technical Field

[0001] The present invention relates to the technical field of 3D printing generative design, and in particular to a vibration mode programmable 3D printing dot matrix generative design method. Background Art

[0002] Metal 3D printed lattices have the performance advantages of being lightweight, high-strength, and reducing vibration and noise. They are being used more and more widely in aerospace, underwater diving, new energy vehicles and other fields. For example, the tail wing of a high-Mach aircraft uses a 3D printed lattice structure, which can effectively reduce weight while maintaining an aerodynamic shape, thereby increasing flight speed and endurance. The electro-hydraulic brake of an underwater submersible uses a 3D printed lattice structure, which can integrate large-scale dispersed valve blocks and pipelines into one, greatly reducing the space occupied by the brake, and reducing the impact generated during hydraulic switching, thereby reducing the working noise of the submersible. The thermal management system on a car uses a large surface area TPMS lattice, combined with a non-uniform lattice design based on heat flow, which can increase the heat dissipation efficiency of the radiator and extend the service life of new energy vehicles.

[0003] During the flight of the above-mentioned aircraft, random vibrations will occur due to factors such as air flow fluctuations, engine operation, and cabin separation; when spacecraft are in orbit, simple harmonic vibrations will occur due to the influence of microgravity and solar radiation; when submarines are sailing underwater, impact vibrations will occur due to the impact of water flow and propeller rotation; during the driving of new energy vehicles, uneven roads and engine vibrations will cause multi-type composite vibrations of the vehicle. The anti-vibration performance of the structural parts after lattice filling, the impact on the vibration mode of the whole machine, and whether the lattice fails under vibration are important contents that need to be considered when designing sports tools.

[0004] At present, the lattice design for vibration performance still adopts the traditional method based on experience or vibration performance experiments, which cannot achieve fast and accurate lattice optimization and filling. It is the inevitable development direction of the future design of the above-mentioned sports tools to quickly, accurately and intelligently generate qualified lattices under specified boundary conditions and frequency response requirements and smoothly realize the filling of lattices in the design domain of structural parts, which has great application potential and research value. However, there are currently no public reports on the generative design of lattice vibration modes. Based on previous practices, the present invention proposes a relatively systematic generative design method for lattice vibration performance to achieve generative design of lattice cell vibration performance. Summary of the invention

[0005] The purpose of the present invention is to provide a 3D printing dot matrix generative design method with programmable vibration modes in view of the deficiencies in the prior art.

[0006] The object of the present invention is achieved through the following technical solution: a vibration mode programmable 3D printing lattice generative design method, comprising the following steps:

[0007] (1) Add a set of feature points to the simple cubic unit cell structure, define the rod positions of the unit cell structure through the position matrix and connection matrix of the feature points, and obtain a 1 / 8 unit cell structure; mirror the 1 / 8 unit cell structure in three orthogonal directions to generate a complete rod-shaped cell, and establish a unit cell database based on the complete rod-shaped cell;

[0008] (2) Based on the vibration modal theory, the fundamental frequency theoretical model of the lattice cell is derived, and the fundamental frequency theoretical model of the lattice cell is used to obtain the fundamental frequencies of unit cell samples with different unit cell structures in the unit cell database to construct a unit cell structure-fundamental frequency dataset;

[0009] (3) Constructing a structure-baseband inverse design model and using a single-cell structure-baseband data set for training. During the training process, the optimization goal is to minimize the generated loss function and adjust the parameters of the structure-baseband inverse design model to obtain a trained structure-baseband inverse design model.

[0010] (4) Based on the unit cell structure-fundamental frequency data set, high-order frequency simulation is performed using dynamic finite element analysis simulation software to construct a unit cell structure-high-order frequency data set;

[0011] (5) Construct a structure-high-order frequency inference model and use the single-cell structure-high-order frequency dataset for training. During the training process, the optimization goal is to minimize the inference loss function and adjust the parameters of the structure-high-order frequency inference model to obtain a trained structure-high-order frequency inference model.

[0012] (6) Input the specified unit cell fundamental frequency into the trained structure-fundamental frequency inverse design model to generate multiple groups of unit cell structures with the specified unit cell fundamental frequency; input each group of unit cell structures into the trained structure-high-order frequency inference model to obtain multiple orders of high-order frequencies corresponding to each group of unit cell structures, and screen the multiple groups of unit cell structures in order according to the specified high-order frequencies to obtain a group of unit cell structures that meet the vibration modal requirements; wherein the vibration modal requirements are the specified unit cell fundamental frequency and the specified high-order frequency.

[0013] Furthermore, in the unit cell database, each unit cell sample includes the unit cell edge length and volume fraction of the unit cell sample;

[0014] In the unit cell structure-fundamental frequency data set, each unit cell sample includes the unit cell structure of the unit cell sample and its corresponding unit cell fundamental frequency, and the unit cell structure includes the unit cell side length and volume fraction;

[0015] In the unit cell structure-high-order frequency data set, each unit cell sample includes the unit cell structure of the unit cell sample and its corresponding high-order frequency, the unit cell structure includes the unit cell side length and volume fraction, and the high-order frequency includes at least the second-order frequency, the third-order frequency and the fourth-order frequency.

[0016] Furthermore, the step (1) specifically includes the following sub-steps:

[0017] (1.1) Add a set of feature points in the simple cubic unit cell structure; wherein the set of feature points includes 12 edge points and 6 surface points, the 12 edge points are respectively on the 12 edges of the simple cubic unit cell structure, and the 6 surface points are respectively on the 6 surfaces of the simple cubic unit cell structure;

[0018] (1.2) defining the rod positions of the unit cell structure by means of the position matrix and the connection matrix of the feature points to obtain a 1 / 8 unit cell structure; wherein the position matrix of the feature points is used to define the positions of the feature points, and the connection matrix of the feature points is used to define the connection conditions of the feature points;

[0019] (1.3) The 1 / 8 unit cell structure is mirrored in three orthogonal directions. After the three mirrorings are completed, the isolated rods and dense rods are filtered out by the connectivity algorithm to obtain a complete rod-shaped cell, and a unit cell database is established based on the complete rod-shaped cell; wherein the connectivity algorithm requires that each end point of the rod is connected to at least two rods; the implementation standard of the isolated rod is that after three mirrorings, at least one end point of the rod is not connected to other rods; the implementation standard of the dense rod is that the average value of the minimum distance between the two pairs of end points of the two rods is less than 4R, where R is the radius of the rod.

[0020] Furthermore, the step (2) specifically includes the following sub-steps:

[0021] (2.1) Obtaining mechanical properties characteristics of a unit cell sample in a unit cell database; wherein the mechanical properties characteristics of the unit cell sample include the mass and equivalent stiffness of the unit cell sample;

[0022] (2.2) Based on the vibration modal theory, the fundamental frequency theoretical model of the lattice cell is derived, and it is corrected according to the volume fraction of the unit cell sample to obtain the corrected fundamental frequency theoretical model;

[0023] (2.3) Inputting the mechanical property characteristics of the unit cell sample obtained in step (2.1) into the modified fundamental frequency theoretical model to obtain the unit cell fundamental frequency of the unit cell sample;

[0024] (2.4) Repeat steps (2.1) to (2.3) until the cell fundamental frequencies of all cell samples with different cell structures in the cell database are obtained, and a cell structure-fundamental frequency dataset is constructed based on the cell fundamental frequencies of all cell samples.

[0025] Furthermore, the fundamental frequency theoretical model of the lattice cell is expressed as:

[0026]

[0027] in, represents the first-order fundamental frequency of the lattice cell, represents the equivalent stiffness of the lattice cell, and m represents the mass of the lattice cell;

[0028] The expression of the modified fundamental frequency theoretical model is:

[0029]

[0030] in, represents the fundamental frequency of the single cell sample, Represents the volume fraction of the unit cell sample.

[0031] Furthermore, the structure-fundamental frequency inverse design model includes a coding space vector predictor and a conditional diffusion model; the unit cell fundamental frequency is input into the structure-fundamental frequency inverse design model, and the corresponding coding space vector is first obtained through the coding space vector predictor, wherein the coding space vector predictor adopts the encoder part in the variational autoencoder network architecture; then the coding space vector is input as a condition into the conditional diffusion model to generate multiple groups of unit cell structures with different unit cell side lengths and volume fractions with specified unit cell fundamental frequencies.

[0032] Furthermore, the training is performed using a unit cell structure-base frequency data set, wherein minimizing the generated loss function is used as an optimization goal during the training process, and the parameters of the structure-base frequency inverse design model are adjusted to obtain a trained structure-base frequency inverse design model, specifically including:

[0033] The unit cell fundamental frequency of each unit cell sample in the unit cell structure-fundamental frequency data set is input into the structure-fundamental frequency inverse design model, and the corresponding encoding space vector is first obtained through the encoding space vector predictor; then the encoding space vector and the unit cell side length and volume fraction corresponding to the unit cell sample in the unit cell structure-fundamental frequency data set are input into the conditional diffusion model together to obtain the corresponding specific unit cell structure, that is, the predicted unit cell side length and volume fraction;

[0034] The unit cell side length and volume fraction of each unit cell sample in the unit cell structure-fundamental frequency data set are taken as the true label; the root mean square error of the unit cell side length is calculated according to the predicted unit cell side length and its corresponding true label, the root mean square error of the volume fraction is calculated according to the predicted volume fraction and its corresponding true label, and the sum of the root mean square error of the unit cell side length and the root mean square error of the volume fraction is calculated as the generation loss function; with minimizing the generation loss function as the optimization goal, the parameters of the structure-fundamental frequency inverse design model are adjusted until the preset training rounds are reached or the error is less than the preset error threshold, so as to obtain a trained structure-fundamental frequency inverse design model.

[0035] Furthermore, the step (4) specifically includes the following sub-steps:

[0036] (4.1) For each single cell sample in the single cell structure-base frequency dataset, obtain its stp format entity model or x_t format entity model;

[0037] (4.2) Using dynamic finite element analysis simulation software to perform finite element simulation of the high-order frequency of the unit cell structure on the stp format solid model or x_t format solid model of the unit cell sample to obtain the high-order frequency of the unit cell sample; wherein the high-order frequency includes at least the second-order frequency, the third-order frequency and the fourth-order frequency;

[0038] (4.3) Construct a single cell structure-high-order frequency dataset based on the single cell structures of all single cell samples and their corresponding high-order frequencies.

[0039] Furthermore, the structure-high-order frequency inference model includes a feature extractor and at least three fully connected neural networks; wherein the feature extractor includes multiple convolutional layers, and the feature extractor is used to extract the structural feature vector of the unit cell structure; the fully connected neural network includes a ReLu activation function layer, a Sigmoid activation function layer and a fully connected layer, and the fully connected neural network is used to normalize the implicit variables in the structural feature vector to obtain high-order frequencies of corresponding orders; each of the fully connected neural networks corresponds to a high-order frequency of one order.

[0040] Furthermore, the single cell structure-high-order frequency data set is used for training, and during the training process, the parameters of the structure-high-order frequency reasoning model are adjusted with minimizing the reasoning loss function as the optimization goal to obtain a trained structure-high-order frequency reasoning model, specifically including:

[0041] The single cell structure of each single cell sample in the single cell structure-high-order frequency data set is input into the structure-high-order frequency inference model, and the corresponding structural feature vector is first obtained through the feature extractor; then the structural feature vector is input into at least three fully connected neural networks respectively to obtain the high-order frequency of the corresponding order;

[0042] The high-order frequency of the single-cell sample in the single-cell structure-high-order frequency dataset is taken as the true label, and the high-order frequency of the corresponding order output by the structure-high-order frequency inference model is taken as the predicted value; the root mean square error of the order is calculated according to the predicted value of the high-order frequency and the true label of the corresponding order, and the sum of the root mean square errors of all orders is calculated as the inference loss function; with minimizing the inference loss function as the optimization goal, the parameters of the structure-high-order frequency inference model are adjusted until the preset training round is reached or the error is less than the preset error threshold, so as to obtain a trained structure-high-order frequency inference model.

[0043] The beneficial effects of the present invention are as follows: the generative design of the present invention is inseparable from a high-value unit cell structure-vibration mode data set. By adopting a high-throughput finite element simulation method, a data set with a large number of samples is generated, providing a large-scale data set for generative design; the present invention derives a fundamental frequency theoretical model of a lattice cell on the basis of traditional vibration mode theory, and further modifies and optimizes it, and uses the modified fundamental frequency theoretical model to extract the main structural parameters of the unit cell structure that affect the vibration mode, and uses this as prior knowledge to introduce it into the structure-fundamental frequency inverse design model, and conducts generative training thereof, which is beneficial to improving the accuracy of unit cell structure generation, and further accelerates the training of the structure-high-order frequency reasoning model; the present invention adopts reverse generation of a structure that satisfies a first-order vibration mode, and then filters the generated unit cell structure according to the order of the vibration mode to find a structure that meets the high-order vibration frequency; the present invention can artificially set the vibration mode, and then hand it over to the structure-fundamental frequency inverse design model and the structure-high-order frequency reasoning model to generate a unit cell structure that meets the set vibration mode; the present invention realizes the generative design of the vibration mode of the unit cell, and the accuracy error is less than 20% after testing. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flow chart of the vibration mode programmable 3D printing lattice generative design method of the present invention;

[0045] Figure 2 is a flow chart of constructing a unit cell structure-base frequency data set of the present invention;

[0046] Figure 3 is a flow chart of constructing a unit cell structure-high-order frequency data set of the present invention;

[0047] Figure 4 is a network architecture flow chart of the structure-baseband reverse design model of the present invention;

[0048] Figure 5 It is a flow chart of the training and application of the structure-high-order frequency inference model of the present invention. DETAILED DESCRIPTION

[0049] Exemplary embodiments will be described in detail herein, examples of which are shown in the accompanying drawings. When the following description refers to the drawings, the same numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Instead, they are merely examples of devices and methods consistent with some aspects of the present invention as detailed in the appended claims.

[0050] The terms used in the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The singular forms "a", "the" and "the" used in the present invention and the appended claims are also intended to include plural forms unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0051] It should be understood that although the terms first, second, third, etc. may be used in the present invention to describe various information, these information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present invention, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0052] The present invention is described in detail below in conjunction with the accompanying drawings. In the absence of conflict, the features of the following embodiments and implementations can be combined with each other.

[0053] See also Figure 1 The vibration mode programmable 3D printing lattice generative design method of the present invention specifically comprises the following steps:

[0054] (1) A set of feature points is added to the simple cubic unit cell structure, and the rod positions of the unit cell structure are defined by the position matrix and connection matrix of the feature points to obtain a 1 / 8 unit cell structure. The 1 / 8 unit cell structure is mirrored in three orthogonal directions to generate a complete rod-shaped cell, and a unit cell database is established based on the complete rod-shaped cell.

[0055] (1.1) Add a set of feature points in the simple cubic unit cell structure. The set of feature points includes 12 edge points and 6 surface points. The 12 edge points are on the 12 edges of the simple cubic unit cell structure, and the 6 surface points are on the 6 surfaces of the simple cubic unit cell structure.

[0056] (1.2) The rod positions of the unit cell structure are defined by the position matrix and connection matrix of the feature points to obtain a 1 / 8 unit cell structure. The position matrix of the feature points is used to define the positions of the feature points, and the connection matrix of the feature points is used to define the connection of the feature points. The shape of the position matrix tensor of the feature points is (18,3), which means that the position matrix tensor has two dimensions. The value of the first dimension is 18, which means that there are 18 feature points; the value of the second dimension is 3, which represents the three-dimensional orthogonal coordinate value of each feature point. The shape of the connection matrix tensor of the feature points is (18,18), which means that the connection matrix tensor has two dimensions. The values ​​of the first and second dimensions are both 18, which represents the connection between the 18 feature points. For example, X(i,j) represents the connection between the i-th feature point and the j-th feature point. If the value of X(i,j) is 1, it means that the i-th feature point and the j-th feature point are connected; if the value of X(i,j) is 0, it means that the i-th feature point and the j-th feature point are not connected.

[0057] (1.3) The 1 / 8 unit cell structure is mirrored in three orthogonal directions. After the three mirrorings are completed, the isolated rods and dense rods are filtered out by the connectivity algorithm to obtain a complete rod-shaped cell, and a unit cell database is established based on the complete rod-shaped cell. Among them, the connectivity algorithm requires that each end of the rod is connected to at least two rods; the implementation standard of the isolated rod is that after three mirrorings, at least one end of the rod is not connected to other rods; the implementation standard of the dense rod is that the average value of the minimum distance between the two pairs of end points of the two rods is less than 4R, where R is the radius of the rod.

[0058] It should be understood that after the mirroring is completed, the rods are very close to each other, resulting in a high rod density in the local area. Even the farthest distance between the bottom surfaces of two rods is less than the sum of the diameters of the two rods, which means that these rods are dense rods. Therefore, they need to be filtered out through the existing connectivity algorithm. Similarly, isolated rods also need to be filtered out through the existing connectivity algorithm.

[0059] Specifically, in this embodiment, the lattice unit cell includes 8 vertices, and these 8 vertices are connected according to their inherent connection mode to form a simple cubic unit cell structure. A set of feature points is added to the simple cubic unit cell structure, and the feature points can move along the edge, surface or body of the simple cubic unit cell structure. Therefore, after determining the position matrix and connection matrix of the feature points, the rod position of the unit cell structure can be determined to obtain a 1 / 8 unit cell structure; wherein, the feature points move along the edge, surface or body of the simple cubic unit cell structure, which depends on the nature of the feature points, that is, whether the feature points are edge points, surface points or body points. For example, edge points can move on the corresponding edge with one degree of freedom; surface points can move on the corresponding surface with two degrees of freedom. Afterwards, the 1 / 8 unit cell structure is mirrored in three orthogonal directions, that is, the 1 / 8 unit cell structure needs to be three times axially symmetric through the three orthogonal directions of x, y, and z, and finally a complete rod-shaped cell is generated. A complete rod-shaped cell is a unit cell sample. Through the above process, multiple unit cell samples can be constructed, and then a unit cell database is constructed based on these unit cell samples.

[0060] Furthermore, in the unit cell database, each unit cell sample includes the unit cell edge length and volume fraction of the unit cell sample.

[0061] (2) Based on the traditional vibration modal theory, the fundamental frequency theoretical model of the lattice cell is derived, and the fundamental frequency theoretical model of the lattice cell is used to obtain the fundamental frequency of the unit cell samples with different unit cell structures in the unit cell database to construct a unit cell structure-fundamental frequency dataset. Figure 2 As shown, it specifically includes the following sub-steps:

[0062] (2.1) Obtain the mechanical properties of the unit cell sample in the unit cell database, where the mechanical properties of the unit cell sample include the mass and equivalent stiffness of the unit cell sample.

[0063] (2.2) Based on the traditional vibration modal theory, the fundamental frequency theoretical model of the lattice cell is derived, and it is corrected according to the volume fraction of the unit cell sample to obtain the corrected fundamental frequency theoretical model.

[0064] It should be understood that traditional vibration modal theory is the theoretical knowledge of vibration modes, including but not limited to: a certain vibration mode has a certain frequency, formation and amplitude, there are linear vibrations, nonlinear vibrations, free vibrations, etc., and vibration modal analysis can be performed through parameter calculation or experimental analysis.

[0065] Furthermore, the fundamental frequency theoretical model of the lattice cell is expressed as:

[0066]

[0067] in, represents the first-order fundamental frequency of the lattice cell, represents the equivalent stiffness of the lattice cell, and m represents the mass of the lattice cell.

[0068] It should be noted that the fundamental frequency of the lattice cell is obtained based on the fundamental frequency theoretical model, and the second, third, fourth and other high-order frequencies of the lattice cell are calculated by the dynamic finite element analysis simulation software. Similarly, the unit cell fundamental frequency of the unit cell sample can be obtained based on the following modified fundamental frequency theoretical model, and then the second, third, fourth and other high-order frequencies corresponding to the unit cell sample can be calculated by the dynamic finite element analysis simulation software based on the unit cell fundamental frequency of the unit cell sample.

[0069] Furthermore, the expression of the modified fundamental frequency theoretical model is:

[0070]

[0071] in, represents the fundamental frequency of the single cell sample, Represents the volume fraction of the unit cell sample.

[0072] (2.3) Input the mechanical properties of the unit cell sample obtained in step (2.1) into the modified fundamental frequency theoretical model to obtain the unit cell fundamental frequency of the unit cell sample. The unit cell fundamental frequency refers to the fundamental frequency in the free state without boundary conditions.

[0073] (2.4) Repeat steps (2.1) to (2.3) until the cell fundamental frequencies of all cell samples with different cell structures in the cell database are obtained, and a cell structure-fundamental frequency dataset is constructed based on the cell fundamental frequencies of all cell samples.

[0074] Furthermore, according to the unit cell database constructed in step (1), the unit cell structure of the unit cell sample is known, so the unit cell side length and volume fraction of the unit cell sample are also known, and the mechanical performance characteristics of the unit cell sample can be obtained according to the unit cell structure of the unit cell sample, and then the fundamental frequency can be obtained through the modified fundamental frequency theoretical model, and finally the unit cell structure-fundamental frequency data set is constructed according to the unit cell side length, volume fraction and fundamental frequency of the unit cell sample, where the unit cell side length and volume fraction belong to the unit cell structure. Therefore, in the unit cell structure-fundamental frequency data set, each unit cell sample contains the unit cell structure of the unit cell sample and its corresponding unit cell fundamental frequency, and the unit cell structure contains the unit cell side length and volume fraction.

[0075] (3) Construct a structure-baseband inverse design model and use the single-cell structure-baseband data set for training. During the training process, the optimization goal is to minimize the generated loss function and adjust the parameters of the structure-baseband inverse design model to obtain a trained structure-baseband inverse design model.

[0076] Furthermore, if Figure 4 As shown, the structure-fundamental frequency inverse design model includes a coding space vector predictor and a conditional diffusion model. Specifically, the unit cell fundamental frequency is input into the structure-fundamental frequency inverse design model, and the corresponding coding space vector is first obtained by the coding space vector predictor, wherein the coding space vector predictor adopts the encoder part in the variational autoencoder (VAE) network architecture; then the coding space vector is input as a condition into the conditional diffusion model to generate multiple groups of unit cell structures with different unit cell side lengths and volume fractions with specified unit cell fundamental frequencies.

[0077] It should be understood that the VAE network is a variational autoencoder, which consists of an encoder part and a decoder part. In this embodiment, the encoder part is used to construct a coding space vector predictor. In this embodiment, an existing publicly available conditional diffusion model is used. The conditional diffusion model is a type of generation model based on a diffusion process. Conditional inputs are introduced into the generation process, such as text descriptions, category labels, or other forms of prior information, to guide the generated unit cell structure to develop in a direction that meets the conditions, and finally generate a unit cell structure that better meets specific needs.

[0078] It should be noted that the fundamental frequency theoretical model of the lattice cell derived in step (2) is added to the structure-fundamental frequency inverse design model as prior knowledge. In addition, the prior knowledge also includes the relationship between the unit cell fundamental frequency and the lattice equivalent elastic modulus and equivalent density. Among them, the unit cell fundamental frequency of the unit cell structure is directly related to its equivalent elastic modulus and equivalent density. The fundamental frequency theoretical model is usually calculated by converting the unit cell structure characteristic data into equivalent elastic modulus and equivalent density; the equivalent elastic modulus is obtained by calculating the equivalent properties of the unit cell with periodic boundary conditions. The periodic boundary conditions refer to: when calculating the equivalent elastic modulus of the unit cell, whether it is considered as an isolated unit cell, but it is assumed that there are countless unit cells around it in three orthogonal directions. Under such premise, its unit cell equivalent properties are calculated, which can be directly solved by the comsol software.

[0079] Furthermore, a single cell structure-base frequency dataset is used for training. During the training process, minimizing the generated loss function is used as the optimization goal, and the parameters of the structure-base frequency inverse design model are adjusted to obtain a trained structure-base frequency inverse design model, specifically including: inputting the single cell base frequency of each single cell sample in the single cell structure-base frequency dataset into the structure-base frequency inverse design model, first passing through the encoding space vector predictor to obtain the corresponding encoding space vector; then inputting the encoding space vector and the single cell side length and volume fraction corresponding to the single cell sample in the single cell structure-base frequency dataset into the conditional diffusion model to obtain the corresponding specific single cell structure, that is, the predicted single cell side length and volume fraction. The cell side length and volume fraction of each cell sample in the cell structure-fundamental frequency dataset are taken as the true label; the root mean square error (RMSE) of the cell side length is calculated according to the predicted cell side length and its corresponding true label, the root mean square error of the volume fraction is calculated according to the predicted volume fraction and its corresponding true label, and the sum of the root mean square error of the cell side length and the root mean square error of the volume fraction is calculated as the generation loss function; with minimizing the generation loss function as the optimization goal, the parameters of the structure-fundamental frequency inverse design model are adjusted until the preset training rounds are reached or the error is less than the preset error threshold, so as to obtain a trained structure-fundamental frequency inverse design model.

[0080] It should be understood that by inputting the unit cell fundamental frequency into the trained structure-fundamental frequency inverse design model, multiple groups of unit cell structures with different unit cell side lengths and volume fractions can be obtained. Therefore, in the training process of the structure-fundamental frequency inverse design model, the encoding space vector output by the encoding space vector predictor and the unit cell side length and volume fraction corresponding to the unit cell sample need to be input into the conditional diffusion model together to obtain a specific unit cell structure with a specified unit cell side length and volume fraction. This has the uniqueness of the training sample, which is convenient for calculating the generation loss function in the subsequent steps, and then helps to adjust the parameters of the structure-fundamental frequency inverse design model during the training process.

[0081] It should be noted that after obtaining the trained structure-fundamental frequency inverse design model, it can also be verified. When verifying the trained structure-fundamental frequency inverse design model, input the unit cell structure generated by the specified unit cell fundamental frequency, and then use the dynamic finite element analysis simulation software to simulate the fundamental frequency of the unit cell structure. If the error between the simulated fundamental frequency and the specified unit cell fundamental frequency is less than the preset error threshold, such as 1e -3 , then the trained structure-base frequency inverse design model is considered accurate.

[0082] (4) Based on the unit cell structure-base frequency data set, high-order frequency simulation is performed through dynamic finite element analysis simulation software to construct a unit cell structure-high-order frequency data set. Figure 3 As shown, the specific steps include:

[0083] (4.1) For each single cell sample in the single cell structure-fundamental frequency dataset, obtain its stp format entity model or x_t format entity model.

[0084] (4.2) Use dynamic finite element analysis simulation software to perform finite element simulation of the high-order frequency of the unit cell structure on the stp format solid model or x_t format solid model of the unit cell sample to obtain the high-order frequency of the unit cell sample. The high-order frequency includes at least the second-order frequency, the third-order frequency and the fourth-order frequency.

[0085] Furthermore, dynamic finite element analysis simulation software includes but is not limited to: ANSYS software, ABAQUS software, COMSOL software and other general commercial software.

[0086] It should be understood that when using dynamic finite element analysis simulation software for simulation, for example, 50 nodes can be used in parallel to implement finite element simulation of high-order frequencies of the structure, and the high-order frequencies of the unit cell sample can be obtained through simulation; wherein, the simulation result is the vibration modes of each order of the specific unit cell structure, the parameter conditions selected during the simulation are the structural parameters of the unit cell, and the result is the frequency of the corresponding order.

[0087] (4.3) Construct a single cell structure-high-order frequency dataset based on the single cell structures of all single cell samples and their corresponding high-order frequencies.

[0088] Furthermore, in the unit cell structure-high-order frequency data set, each unit cell sample includes the unit cell structure of the unit cell sample and its corresponding high-order frequency. The unit cell structure includes the unit cell edge length and volume fraction, and the high-order frequency includes at least three orders of high-order frequencies: second-order frequency, third-order frequency and fourth-order frequency.

[0089] (5) Construct a structure-high-order frequency inference model and use the single-cell structure-high-order frequency dataset for training. During the training process, the optimization goal is to minimize the inference loss function and adjust the parameters of the structure-high-order frequency inference model to obtain a trained structure-high-order frequency inference model.

[0090] Furthermore, if Figure 5 As shown, the structure-high-order frequency inference model includes a feature extractor and at least three fully connected neural networks, wherein the feature extractor includes multiple convolutional layers, and the feature extractor is used to extract the structural feature vector of the unit cell structure; the fully connected neural network includes a ReLu activation function layer, a Sigmoid activation function layer and a fully connected layer, and the fully connected neural network is used to normalize the implicit variables in the structural feature vector to obtain the high-order frequencies of the corresponding order; each fully connected neural network corresponds to a high-order frequency of one order.

[0091] Furthermore, a single-cell structure-high-order frequency data set is used for training. During the training process, the parameters of the structure-high-order frequency inference model are adjusted with the minimization of the inference loss function as the optimization goal to obtain a trained structure-high-order frequency inference model, specifically including: inputting the single-cell structure of each single-cell sample in the single-cell structure-high-order frequency data set into the structure-high-order frequency inference model, first obtaining the corresponding structural feature vector through the feature extractor; then inputting the structural feature vectors into at least three fully connected neural networks respectively to obtain the high-order frequency of the corresponding order. The high-order frequency of the single-cell sample in the single-cell structure-high-order frequency data set is used as the true label, and the high-order frequency of the corresponding order output by the structure-high-order frequency inference model is used as the predicted value. The root mean square error of the order is calculated according to the predicted value of the high-order frequency and the true label of the corresponding order, and the sum of the root mean square errors of all orders is calculated as the inference loss function; with the minimization of the inference loss function as the optimization goal, the parameters of the structure-high-order frequency inference model are adjusted until the preset training round is reached or less than the preset error threshold, and the trained structure-high-order frequency inference model is obtained.

[0092] It should be noted that, in this embodiment, the single cell structure-high-order frequency data set can also be randomly divided into a training set and a validation set. For example, 5%-10% of the sample size in the single cell structure-high-order frequency data set is selected as the validation set, and the remaining single cell samples are used as the training set; the training set is then used to perform the above-mentioned training process on the structure-high-order frequency inference model; the trained structure-high-order frequency inference model is then verified using the validation set. During the verification process, the mean square error (MSE) can be used to evaluate the accuracy of the structure-high-order frequency inference model. In addition, the parameters of the structure-high-order frequency inference model can be fine-tuned according to the mean square error; finally, the final structure-high-order frequency inference model that has been verified is used to obtain the corresponding order of the high-order frequency of the specified single cell structure. For example, the structural feature vector output by the feature extractor is input into the second fully connected neural network to obtain the third-order frequency corresponding to the single cell structure, such as Figure 5 shown.

[0093] (6) Input the specified unit cell fundamental frequency into the trained structure-fundamental frequency inverse design model to generate multiple groups of unit cell structures with the specified unit cell fundamental frequency; input each group of unit cell structures into the trained structure-high-order frequency inference model to obtain multiple orders of high-order frequencies corresponding to each group of unit cell structures, and screen the multiple groups of unit cell structures in order according to the specified high-order frequencies to obtain a group of unit cell structures that meet the vibration mode requirements, such as Figure 1 As shown in the figure. The vibration mode requirements are the specified unit cell fundamental frequency and the specified high-order frequency.

[0094] Specifically, in order to obtain a unit cell structure that meets the vibration modal requirements, the vibration mode refers to frequencies of different orders, and the vibration modal requirements refer to the specified unit cell fundamental frequency, second-order frequency, third-order frequency, fourth-order frequency and other multiple-order high-order frequencies. First, the specified unit cell fundamental frequency is input into the trained structure-fundamental frequency inverse design model, and multiple groups of unit cell structures with the specified unit cell fundamental frequency can be generated. These multiple groups of unit cell structures meet the requirements of the unit cell fundamental frequency in the vibration modal requirements. Then, for each group of unit cell structures, it is input into the trained structure-high-order frequency inference model, and the second-order frequency, third-order frequency, fourth-order frequency and other multiple-order high-order frequencies corresponding to the group of unit cell structures can be obtained; repeat the process again to obtain the second-order frequency, third-order frequency, fourth-order frequency and other multiple-order high-order frequencies corresponding to multiple groups of unit cell structures. Secondly, multiple groups of unit cell structures are filtered and screened according to the specified second-order frequency. Specifically, the error between the second-order frequency of multiple groups of unit cell structures and the specified second-order frequency is calculated. If the error is greater than the preset second-order frequency error threshold, the group of unit cell structures corresponding to the error is filtered out. Similarly, multiple groups of unit cell structures are filtered according to the specified second-order frequency to obtain multiple groups of unit cell structures remaining after the second-order frequency screening. After that, the multiple groups of unit cell structures remaining after the second-order frequency screening are filtered and screened according to the specified third-order frequency. Specifically, the error between the third-order frequency of multiple groups of unit cell structures and the specified third-order frequency is calculated. If the error is greater than the preset third-order frequency error threshold, the group of unit cell structures corresponding to the error is filtered out. Similarly, multiple groups of unit cell structures remaining after the second-order frequency screening are filtered according to the specified third-order frequency to obtain multiple groups of unit cell structures remaining after the third-order frequency screening. Similarly, the multiple groups of unit cell structures remaining after the previous screening are filtered in order according to the specified fourth-order frequency and other multiple-order high-order frequencies, and finally a group of unit cell structures that meet the vibration mode requirements are obtained, which means that the design is completed.

[0095] It should be noted that, based on the trained structure-fundamental frequency inverse design model, multiple groups of unit cell structures with specified fundamental frequencies are generated, and these multiple groups of unit cell structures have attribute labels of density or porosity.

[0096] In summary, the generative design of the present invention is inseparable from the high-value unit cell structure-vibration mode data set. By adopting a high-throughput finite element simulation method, a data set with a large number of samples is generated, providing a large-scale data set for generative design; the present invention derives the fundamental frequency theoretical model of the lattice cell on the basis of the traditional vibration mode theory, and further modifies and optimizes it, and uses the modified fundamental frequency theoretical model to extract the main structural parameters of the unit cell structure that affect the vibration mode, and uses this as prior knowledge to import into the structure-fundamental frequency inverse design model, and conducts its generative training, which is beneficial to improve the accuracy of unit cell structure generation, and then accelerates the training of the structure-high-order frequency reasoning model; the present invention adopts the reverse generation of the structure that satisfies the first-order vibration mode, and then filters the generated unit cell structure according to the order of the vibration mode to find the structure that meets the high-order vibration frequency; the present invention can artificially set the vibration mode, and then hand it over to the structure-fundamental frequency inverse design model and the structure-high-order frequency reasoning model to generate a unit cell structure that meets the set vibration mode; the present invention realizes the generative design of the vibration mode of the unit cell, and the accuracy error is less than 20% after testing.

[0097] The above is only a preferred implementation case of the present invention and does not limit the present invention in any form. Although the implementation process of the present invention is described in detail above, for those familiar with the art, they can still modify the technical solutions recorded in the above examples, or replace some of the technical features therein with equivalents. All modifications, equivalent replacements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A vibration mode programmable 3D printing lattice generative design method, characterized in that: The following steps are involved: (1) Add a set of feature points to the simple cubic unit cell structure, define the rod positions of the unit cell structure through the position matrix and connection matrix of the feature points, and obtain a 1 / 8 unit cell structure; mirror the 1 / 8 unit cell structure in three orthogonal directions to generate a complete rod-shaped cell, and establish a unit cell database based on the complete rod-shaped cell; (2) on the basis of vibration modal theory, a fundamental frequency theoretical model of the lattice cell is derived, and the fundamental frequency theoretical model of the lattice cell is used to obtain the fundamental frequencies of unit cell samples with different unit cell structures in the unit cell database, so as to construct a unit cell structure-fundamental frequency data set; the step (2) specifically includes the following sub-steps: (2.1) Obtaining mechanical properties characteristics of a unit cell sample in a unit cell database; wherein the mechanical properties characteristics of the unit cell sample include the mass and equivalent stiffness of the unit cell sample; (2.2) Based on the vibration modal theory, the fundamental frequency theoretical model of the lattice cell is derived, and it is corrected according to the volume fraction of the unit cell sample to obtain a corrected fundamental frequency theoretical model; the expression of the corrected fundamental frequency theoretical model is: Among them, f1 ′ represents the fundamental frequency of the unit cell sample, a represents the volume fraction of the unit cell sample, represents the equivalent stiffness of the lattice cell, and m represents the mass of the lattice cell; (2.3) inputting the mechanical performance characteristics of the unit cell sample obtained in step (2.1) into the modified fundamental frequency theoretical model to obtain the unit cell fundamental frequency of the unit cell sample; (2.4) Repeat steps (2.1) to (2.3) until the cell fundamental frequencies of all cell samples with different cell structures in the cell database are obtained, and a cell structure-fundamental frequency dataset is constructed based on the cell fundamental frequencies of all cell samples; (3) constructing a structure-baseband inverse design model and using a unit cell structure-baseband data set for training. During the training process, the optimization goal is to minimize the generated loss function and adjust the parameters of the structure-baseband inverse design model to obtain a trained structure-baseband inverse design model; (4) Based on the unit cell structure-fundamental frequency data set, high-order frequency simulation is performed using dynamic finite element analysis simulation software to construct a unit cell structure-high-order frequency data set; (5) constructing a structure-high-order frequency inference model and using a single-cell structure-high-order frequency dataset for training. During the training process, the optimization goal is to minimize the inference loss function and adjust the parameters of the structure-high-order frequency inference model to obtain a trained structure-high-order frequency inference model. (6) Input the specified unit cell fundamental frequency into the trained structure-fundamental frequency inverse design model to generate multiple groups of unit cell structures with the specified unit cell fundamental frequency; input each group of unit cell structures into the trained structure-high-order frequency inference model to obtain multiple orders of high-order frequencies corresponding to each group of unit cell structures, and screen the multiple groups of unit cell structures in order according to the specified high-order frequencies to obtain a group of unit cell structures that meet the vibration modal requirements; wherein the vibration modal requirements are the specified unit cell fundamental frequency and the specified high-order frequency.

2. The vibration mode programmable 3D printing lattice generative design method according to claim 1, characterized in that: In the unit cell database, each unit cell sample includes the unit cell side length and volume fraction of the unit cell sample; In the unit cell structure-fundamental frequency data set, each unit cell sample includes the unit cell structure of the unit cell sample and its corresponding unit cell fundamental frequency, and the unit cell structure includes the unit cell side length and volume fraction; In the unit cell structure-high-order frequency data set, each unit cell sample includes the unit cell structure of the unit cell sample and its corresponding high-order frequency, the unit cell structure includes the unit cell side length and volume fraction, and the high-order frequency includes at least the second-order frequency, the third-order frequency and the fourth-order frequency.

3. The vibration mode programmable 3D printing lattice generative design method according to claim 1, characterized in that: The step (1) specifically includes the following sub-steps: (1.1) Add a set of feature points in the simple cubic unit cell structure; wherein the set of feature points includes 12 edge points and 6 surface points, the 12 edge points are respectively on the 12 edges of the simple cubic unit cell structure, and the 6 surface points are respectively on the 6 surfaces of the simple cubic unit cell structure; (1.2) defining the rod positions of the unit cell structure by means of the position matrix and the connection matrix of the feature points to obtain a 1 / 8 unit cell structure; wherein the position matrix of the feature points is used to define the positions of the feature points, and the connection matrix of the feature points is used to define the connection conditions of the feature points; (1.3) The 1 / 8 unit cell structure is mirrored in three orthogonal directions. After the three mirrorings are completed, the isolated rods and dense rods are filtered out by the connectivity algorithm to obtain a complete rod-shaped cell, and a unit cell database is established based on the complete rod-shaped cell; wherein the connectivity algorithm requires that each end point of the rod is connected to at least two rods; the implementation standard of the isolated rod is that after three mirrorings, at least one end point of the rod is not connected to other rods; the implementation standard of the dense rod is that the average value of the minimum distance between the two pairs of end points of two rods is less than 4R, where R is the radius of the rod.

4. The vibration mode programmable 3D printing lattice generative design method according to claim 1, characterized in that: The expression of the fundamental frequency theoretical model of the lattice cell is: Among them, f1 represents the first-order fundamental frequency of the lattice cell, represents the equivalent stiffness of the lattice cell, and m represents the mass of the lattice cell.

5. The vibration mode programmable 3D printing lattice generative design method according to claim 1, characterized in that: The structure-fundamental frequency inverse design model includes a coding space vector predictor and a conditional diffusion model; the unit cell fundamental frequency is input into the structure-fundamental frequency inverse design model, and the corresponding coding space vector is first obtained through the coding space vector predictor, wherein the coding space vector predictor adopts the encoder part in the variational autoencoder network architecture; then the coding space vector is input as a condition into the conditional diffusion model to generate multiple groups of unit cell structures with different unit cell side lengths and volume fractions with specified unit cell fundamental frequencies.

6. The vibration mode programmable 3D printing lattice generative design method according to claim 1, characterized in that: The unit cell structure-base frequency data set is used for training, and during the training process, the minimization of the generated loss function is taken as the optimization goal, and the parameters of the structure-base frequency inverse design model are adjusted to obtain the trained structure-base frequency inverse design model, which specifically includes: The unit cell fundamental frequency of each unit cell sample in the unit cell structure-fundamental frequency data set is input into the structure-fundamental frequency inverse design model, and the corresponding encoding space vector is first obtained through the encoding space vector predictor; then the encoding space vector and the unit cell side length and volume fraction corresponding to the unit cell sample in the unit cell structure-fundamental frequency data set are input into the conditional diffusion model together to obtain the corresponding specific unit cell structure, that is, the predicted unit cell side length and volume fraction; The unit cell side length and volume fraction of each unit cell sample in the unit cell structure-fundamental frequency data set are taken as the true label; the root mean square error of the unit cell side length is calculated according to the predicted unit cell side length and its corresponding true label, the root mean square error of the volume fraction is calculated according to the predicted volume fraction and its corresponding true label, and the sum of the root mean square error of the unit cell side length and the root mean square error of the volume fraction is calculated as the generation loss function; with minimizing the generation loss function as the optimization goal, the parameters of the structure-fundamental frequency inverse design model are adjusted until the preset training rounds are reached or the error is less than the preset error threshold, so as to obtain a trained structure-fundamental frequency inverse design model.

7. The vibration mode programmable 3D printing lattice generative design method according to claim 1, characterized in that: The step (4) specifically includes the following sub-steps: (4.1) For each single cell sample in the single cell structure-base frequency dataset, obtain its stp format entity model or x_t format entity model; (4.2) using dynamic finite element analysis simulation software to perform finite element simulation of the high-order frequency of the unit cell structure on the stp format solid model or the x_t format solid model of the unit cell sample to obtain the high-order frequency of the unit cell sample; wherein the high-order frequency at least includes the second-order frequency, the third-order frequency and the fourth-order frequency; (4.3) Construct a single cell structure-high-order frequency dataset based on the single cell structures of all single cell samples and their corresponding high-order frequencies.

8. The vibration mode programmable 3D printing lattice generative design method according to claim 1, characterized in that: The structure-high-order frequency inference model includes a feature extractor and at least three fully connected neural networks; wherein the feature extractor includes multiple convolutional layers, and the feature extractor is used to extract the structural feature vector of the unit cell structure; the fully connected neural network includes a ReLu activation function layer, a Sigmoid activation function layer and a fully connected layer, and the fully connected neural network is used to normalize the implicit variables in the structural feature vector to obtain the corresponding order of high-order frequencies; each of the fully connected neural networks corresponds to a high-order frequency of one order.

9. The vibration mode programmable 3D printing lattice generative design method according to claim 1, characterized in that: The single cell structure-high-order frequency data set is used for training. During the training process, the minimization of the inference loss function is used as the optimization goal, and the parameters of the structure-high-order frequency inference model are adjusted to obtain a trained structure-high-order frequency inference model, specifically including: The single cell structure of each single cell sample in the single cell structure-high-order frequency data set is input into the structure-high-order frequency inference model, and the corresponding structural feature vector is first obtained through the feature extractor; then the structural feature vector is input into at least three fully connected neural networks respectively to obtain the high-order frequency of the corresponding order; The high-order frequency of the single-cell sample in the single-cell structure-high-order frequency dataset is taken as the true label, and the high-order frequency of the corresponding order output by the structure-high-order frequency inference model is taken as the predicted value; the root mean square error of the order is calculated according to the predicted value of the high-order frequency and the true label of the corresponding order, and the sum of the root mean square errors of all orders is calculated as the inference loss function; with minimizing the inference loss function as the optimization goal, the parameters of the structure-high-order frequency inference model are adjusted until the preset training round is reached or the error is less than the preset error threshold, so as to obtain a trained structure-high-order frequency inference model.

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