A formation method and use method of a lattice performance evaluation prediction system

Abstract

The present invention relates to a formation method and a use method of a lattice performance evaluation prediction system. The lattice structure is parameterized and input into a lattice performance evaluation model to obtain performance parameters corresponding to the structure parameters. A relative density prediction model is obtained by calculating and training the relative density. The obtained data is then trained through a machine learning model to finally obtain a lattice performance prediction model. In the lattice performance prediction model, the predicted relative density is input as an amplified characteristic parameter for predicting the elastic modulus, so that the prediction of the elastic modulus is more accurate. In addition, a genetic algorithm is introduced to input the expected performance to obtain the lattice structure. The use of this method can select a lattice structure that meets the functional requirements in the conceptual design stage, can realize forward or reverse design, reduce the amount of manual operation and improve the efficiency of lattice structure design, and expand the design space of the mechanical properties of the lattice structure.

Description

Technical Field

[0001] The present invention relates to the technical field of lattice structure design, and in particular to a forming method and a using method of a lattice performance evaluation and prediction system. Background Art

[0002] Additive manufacturing, commonly known as 3D printing, is a manufacturing technology that integrates computer-aided design, material processing and forming technology, and uses software and numerical control systems to stack special metal materials, non-metallic materials and medical biomaterials layer by layer in the form of extrusion, sintering, melting, photocuring, spraying, etc. based on digital model files to produce physical objects; the extremely high manufacturing freedom of additive manufacturing has promoted the development of lightweight structural materials. Further integration of mesoscale lattice materials in structural parts has become the preferred strategy for structural lightweight and functional customization. The reason is that the lattice materials of lattice structures have the advantages of low density, designable structure and customizable functions, and they play an irreplaceable role in many fields such as aviation, aerospace, automobiles, and medical care. In the conceptual stage, designing, evaluating and selecting the mechanical properties of lattice materials with suitable performance is a prerequisite for integrating them into structural parts.

[0003] The design defects of the current lattice structure are mainly the following:

[0004] 1. In the past, lattice material design was usually based on manual iterative trial and error, which required designers and engineers to master additional expertise for iterative design;

[0005] 2. The complexity of lattice materials requires a lot of computational cost for performance analysis and evaluation. In particular, the design process needs to consider the influence of various factors such as the configuration size and morphological characteristics of the lattice material on its mechanical performance;

[0006] 3. The printing accuracy of additive manufacturing is constantly improving, but the design of lattice structures is still limited to simple geometric structures, which undoubtedly limits the effective design space of lattice mechanical properties. Summary of the invention

[0007] The technical problem to be solved by the present invention is to provide a method for forming and using a lattice performance evaluation and prediction system which establishes the relationship between lattice structure parameters and elastic modulus and can conveniently and quickly evaluate and predict.

[0008] The technical solution adopted by the present invention to solve the technical problem is:

[0009] A method for forming a lattice performance evaluation and prediction system, the lattice performance evaluation and prediction system comprising a lattice performance evaluation model, a relative density prediction model and a lattice performance prediction model, the steps of the formation method are:

[0010] S10, forming a lattice performance evaluation model, the lattice performance evaluation model is composed of the following steps;

[0011] S11, according to the specific structure of the lattice to be designed, all structural parameters affecting the lattice structure are obtained to form a structural parameter set;

[0012] S12. Determine the domain value range of each structural parameter according to actual needs;

[0013] S13, sampling is performed within the domain value range of each structural parameter, all different parameters form a corresponding structural parameter set, and N groups of structural parameter sets are obtained through sampling;

[0014] S14, modeling the N sets of structural parameter sets in 3D software to form lattice models of N smooth subdivision surfaces;

[0015] S15, obtaining representative volume units for each lattice model;

[0016] S16. Establishing periodic boundary conditions for each representative volume unit and setting the same material properties, applying equivalent stress, and obtaining the deformation of the corresponding representative volume unit;

[0017] S17, calculating the elastic modulus of each lattice according to the deformation and equivalent stress obtained in step S16;

[0018] S20, the formation of a relative density prediction model, the relative density prediction model is formed by the following steps;

[0019] S21, obtaining N sets of structural parameter sets in step S13 and N lattice models in step S14, setting material density, and calculating the relative density of each lattice model;

[0020] S22, using a multinomial regression model to train the data in step S21 to obtain a relative density prediction model, and optimizing the coefficients of the relative density prediction model by a least squares method;

[0021] S30, forming a lattice performance prediction model, the lattice performance prediction model is formed by the following steps;

[0022] S31, gathering all data forming a lattice performance evaluation model and a relative density prediction model and establishing a relationship between a structure parameter set, a lattice model, deformation of a representative volume unit, relative density, and elastic modulus;

[0023] S32. Use the random forest model to train the data in step S31 to obtain a lattice performance prediction model.

[0024] More specifically, the steps of executing step S16 are:

[0025] S161, the surfaces of the representative volume unit on the XY, YZ and XZ axis planes are defined as principal planes, and the parallel planes opposite to the principal planes are classified as slave planes, and a set of constraint equations in three directions are established on the unit nodes in the principal planes and the slave planes;

[0026] S162. Select the same material input analysis software, batch calculate the deformation of representative volume units, and calculate the deformation of all representative units separately using the following formula:

[0027]

[0028] Among them, u z represents the displacement in the Z direction, δ z represents the deformation in the Z direction, represents the normal strain in the Z direction, RVE size is the length of the representative volume unit in the Z direction when it is not deformed;

[0029] The calculation in the Z direction is consistent.

[0030] More specifically, the calculation formula of the elastic modulus in step S17 is:

[0031]

[0032] Among them, E z Indicates the elastic modulus in the Z direction, F z Indicates the load in the Z direction, A xy Indicates the area used for load, used to calculate stress σ z , δ z represents the deformation in the Z direction, l z It represents the length of the representative volume unit in the Z direction when it is not deformed and is used to calculate the strain ε z .

[0033] More specifically, in step S22, the relative density prediction model is:

[0034]

[0035] Where RD is the relative density, β0 is the intercept, and β i and β ij are the linear and quadratic coefficients, respectively, and X i and X j is a geometric parameter and ε is an error term.

[0036] More specifically, the data in step S21 is divided into two parts, one part is used for model training, and the other part is used for verifying the training results.

[0037] More specifically, in step S32, the lattice performance prediction model is:

[0038]

[0039] Among them, E RF (Z) is the predicted value of elastic modulus, m is the number of decision trees, T j (Z) is the predicted value of the jth decision tree;

[0040] The calculation formula of the decision tree is:

[0041]

[0042] Among them, L is the number of leaf nodes in the decision tree, w i is the predicted value of the i-th leaf node, I(Z∈R i ) is an indicator function indicating whether Z falls into region R i .

[0043] More specifically, in step S32, all data input into the random forest model are randomly divided into two parts, one part is used for model training, and the other part is used to verify the training results; 80% of the data is used for model training, and 20% of the data is used to verify the training results.

[0044] Specifically, by using the mean absolute error MAE, root mean square error RMSE and determination coefficient R 2 To verify the predicted elastic modulus results, the formula is as follows,

[0045]

[0046] Among them, y i is the calculated value of relative density or elastic modulus, is the predicted value of relative density or elastic modulus, m is the number of samples, is the predicted mean response.

[0047] More specifically, a lattice inverse optimization model is set based on the lattice performance prediction model, and the optimization method of the lattice inverse optimization model is:

[0048] S41, determining the domain value range of each structural parameter in the structural parameter set, and determining the elastic modulus and relative density of the target;

[0049] S42, sampling is performed within the domain value range of each structural parameter, all different parameters form a corresponding structural parameter set, and multiple groups of structural parameter sets are obtained through sampling;

[0050] S43, inputting the structural parameters of the multiple groups of structural parameter sets into the lattice performance prediction model and the relative density prediction model to obtain the predicted elastic modulus and relative density corresponding to each structural parameter set;

[0051] S44. Evaluate the quality of each structural parameter set according to the fitness function. The fitness function is:

[0052]

[0053] Among them, V Individual is the structural parameter set, is the elastic modulus predicted by the lattice property prediction model, is the target elastic modulus, RD is the relative density, w1 and w2 are weight coefficients used to adjust the balance between target performance and relative density;

[0054] S45, selecting multiple sets of structural parameter sets according to fitness values ​​using a roulette wheel selection or a tournament selection method;

[0055] S46, for the multiple sets of structure parameter sets, the structure parameters are subjected to crossover operation and / or mutation operation to form multiple new sets of structure parameter sets;

[0056] S47, returning to iterative execution steps S43-S46, until the maximum number of iterations is reached or the fitness value converges, and terminating the operation, so that the absolute deviation between the predicted elastic modulus and the target elastic modulus is minimized and the relative density is minimized.

[0057] To be more specific, the lattice model is a rod-type lattice structure, and its structural parameter set is {Minn, Mout, Mstrut, Msmooth, Tcube}, where Minn is the size of the internal nodes of the lattice unit, Mout is the size of the external nodes of the lattice unit, Mstrut is a parameter that describes the radius size of the lattice unit pillar, Msmooth is a parameter that determines the smoothness of the lattice pillar, and Tcube is a parameter that determines the size of the lattice formed by the internal nodes of the lattice unit.

[0058] To be more specific, in step S14, the modeling method of the lattice model is to first create a rough polygonal mesh surface model, in which the parameters affecting the polygonal mesh surface model correspond one to one with the structural parameters, and then form lattice units according to the specific structural parameters and based on the subdivision surface modeling method, and finally form a lattice structure composed of multiple lattice units to form a lattice model.

[0059] More specifically, in step S13, sampling is performed using a Latin hypercube sampling method.

[0060] A method for using the above-mentioned lattice performance evaluation and prediction system, first, inputting the structural parameters of the lattice structure and the domain value range of the structural parameters into the lattice performance evaluation model, the lattice performance evaluation model outputs multiple groups of structural parameter sets and multiple lattice models to the relative density prediction model to train the lattice relative density prediction model, and at the same time, the lattice performance evaluation model outputs the elastic modulus and the relative density prediction model outputs the relative density to the lattice performance prediction model to train the lattice performance prediction model of the lattice structure, thereby obtaining the relative density prediction model and the lattice performance prediction model of the lattice structure; then, the elastic modulus of the corresponding structural parameter can be given by the lattice performance prediction model, and the structural parameter with greater sensitivity can be adjusted according to the elastic modulus actually required until the corresponding elastic modulus meets the actual requirement.

[0061] A method for using the lattice performance evaluation and prediction system described above, first, the structural parameters of the lattice structure to be designed are directly input into a relative density prediction model and a lattice performance prediction model, the relative density prediction model outputs the predicted relative density and inputs it into the lattice performance prediction model together with the structural parameters, the lattice performance prediction model gives the elastic modulus corresponding to the structural parameters, and the structural parameters with greater sensitivity can be adjusted according to the elastic modulus actually required until the corresponding elastic modulus meets the actual requirements.

[0062] A method for using the above-mentioned lattice performance evaluation and prediction system, first, inputting the target elastic modulus into the lattice inverse optimization model, selecting the lattice model or matching it by the system; the lattice inverse optimization model finally obtains the optimal structural parameter set that meets the target elastic modulus and relative density according to the genetic algorithm in conjunction with the relative density prediction model and the lattice performance prediction model.

[0063] The beneficial effects of the present invention are as follows: by parameterizing the lattice structure and inputting it into a lattice performance evaluation model, an elastic modulus corresponding to the structural parameters is obtained, and at the same time, the relative density is calculated by the structural parameters and trained to obtain a relative density prediction model, and then the structural parameters, elastic modulus and relative density are trained through a random forest model to finally obtain a lattice performance prediction model; in the lattice performance prediction, the structural parameters and the predicted relative density are input as amplified characteristic parameters for predicting the elastic modulus, so that the prediction of the elastic modulus is more accurate, and in addition, a genetic algorithm is introduced to input the expected performance to obtain the lattice structure; the use of this method can select a lattice structure that meets the functional requirements in the conceptual design stage, can realize forward or reverse design, reduce the amount of manual operation and improve the efficiency of lattice structure design, and expand the design space of the mechanical properties of the lattice structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 is a flow chart of a method for forming a lattice performance evaluation and prediction system of the present invention;

[0065] Figure 2 is a schematic diagram of the parameterized lattice structure of the present invention Figure 1 ;

[0066] Figure 3 It is a schematic diagram of the lattice shape corresponding to the change of the structural parameters of the parameterized lattice structure of the present invention;

[0067] Figure 4 It is a schematic diagram of establishing periodic boundary conditions in the present invention;

[0068] Figure 5 It is a schematic diagram of the deformation of the RVE of the present invention in the Z-axis direction;

[0069] Figure 6 is a flow chart of the lattice inverse optimization model of the present invention;

[0070] Figure 7 is a diagram showing the difference in elastic modulus between the lattice structure designed by the present invention and the conventional lattice structure;

[0071] Figure 8 It is the pressure-strain diagram of the BBC of the present invention and the four customized lattices;

[0072] Fig. 9 It is the relationship diagram between the structural parameters and the relative density of the present invention;

[0073] Fig.10 It is the relationship diagram of the structural parameters, relative density and elastic modulus of the present invention;

[0074] Fig.11 It is a difference diagram between the predicted relative density and the actual relative density of the present invention;

[0075] Fig.12 It is a diagram showing the difference between the predicted elastic modulus and the actual elastic modulus of the present invention. DETAILED DESCRIPTION

[0076] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0077] The present application provides a lattice performance evaluation and prediction system, which mainly includes three models, namely a lattice performance evaluation model, a relative density prediction model and a lattice performance prediction model. The lattice performance evaluation model is used to evaluate the performance of a newly input lattice structure (i.e., a lattice structure that is not in the lattice performance prediction model) and generate corresponding associated data; the relative density prediction model obtains the relative density of the newly input lattice structure for calculation and training, and forms a relative density prediction model for the lattice structure; the lattice performance prediction model obtains the associated data output by the lattice performance evaluation model and the relative density obtained by the relative density prediction model and trains, and finally forms a lattice performance prediction model for the lattice structure.

[0078] like Figure 1 The steps of the formation method of the lattice performance evaluation prediction system are as follows:

[0079] S10, the formation of the lattice performance evaluation model mainly includes the following steps:

[0080] S11. First, the designer provides a specific structure of a lattice, and obtains all structural parameters for the lattice structure to form a corresponding structural parameter set, that is, a parameterized lattice structure; here, the specific structure of the lattice can be restored through this structural parameter set; in this application, a rod-type lattice is taken as an example to introduce the lattice shape by defining five key structural parameters as a structural parameter set, and the structural parameter set is {Minn, Mout, Mstrut, Msmooth, Tcube}, where Figure 2 As shown, the internal node size (Minn) is the size of the internal node of the lattice unit; the external node size (Mout) is the size of the external node of the lattice unit; the pillar size (Mstrut) is the radius size describing the pillar of the lattice unit; the smoothness (Msmooth) is the parameter that determines the smoothness of the lattice pillar; the lattice internal skeleton size (Tcube) is the size of the square grid formed by the internal nodes of the lattice unit; the shape is changed by increasing or decreasing the corresponding structural parameters, such as Figure 3 shown.

[0081] The structural parameter set may also be defined according to the actual requirements of the lattice structure. For example, in some lattice structures, the size of the lattice skeleton is not displayed, that is, the structural parameter set of such a lattice is {Minn, Mout, Mstrut, Msmooth}.

[0082] S12. According to the accuracy of the additive manufacturing equipment and the actual design requirements, determine the domain value range under the actual design requirements for each structural parameter; the domain value range here is the range between the minimum value and the maximum value of each structural parameter.

[0083] S13. According to the domain value range of different structural parameters in the structural parameter set, sampling is performed by the Latin hypercube sampling method to obtain N different structural parameter sets; this statistical method helps to sample the five geometric parameters to ensure that the coverage range of each structural parameter is uniform; each structural parameter set corresponds to a different lattice structure; according to the requirements, the specific sampling range of each structural parameter is shown in the following table:

[0084]

[0085] Considering the minimum resolution of the AM equipment, each structural parameter should be rounded to two decimal places, which clearly determines a global design space containing 21 × 21 × 11 × 101 × 6 design possibilities. 280 structural parameter sets were extracted using the Latin hypercube sampling method.

[0086] S14. Modeling N different sets of structural parameters in 3D software, which may be Rhino7-Grasshopper, and forming them into lattice models of N smooth subdivision surfaces; based on the above-mentioned rod-like lattice structure, a total of 280 lattice models of smooth subdivision surfaces are formed.

[0087] The modeling method of the lattice model for the rod-type lattice structure is as follows: first, a rough polygonal mesh surface model is created, and the parameters affecting the polygonal mesh surface model correspond one to one with the structural parameters. Then, lattice units are formed according to the specific structural parameters and based on the subdivision surface modeling (Sub-D) method. Finally, a lattice structure is composed of multiple lattice units to form a lattice model.

[0088] Next, the mechanical properties of the lattice model need to be evaluated. During the numerical analysis, the inherent complexity of the lattice material leads to expensive computational costs. The homogenization method is used to balance computational efficiency and evaluation accuracy. This method treats the lattice material as an equivalent continuous material, simplifying the calculation process. This method allows the use of equivalent material properties to represent the macroscopic behavior of the lattice material, such as elastic modulus, Poisson's ratio, and thermal conductivity. Therefore, the following steps are designed based on the homogenization method.

[0089] S15. Obtain a representative volume element (RVE) for each lattice model; thus, 280 representative volume elements (RVEs) can be obtained. In this embodiment, a cubic RVE is selected, which is composed of a 3×3×3 lattice structure, that is, there are 3 lattice structures arranged in a row in the X-axis, Y-axis and Z-axis directions; the size of the RVE in one direction is 18 mm. This selection ensures stable macroscopic mechanical behavior and minimizes the size effect, which also accelerates the collection of elastic moduli of all lattice models.

[0090] S16. To achieve material uniformity, a periodic boundary condition is established for each representative volume unit and the same material properties are set, and an equivalent stress is applied to obtain the deformation of the corresponding representative volume unit;

[0091] The steps to execute S16 are as follows:

[0092] S161. The surfaces of RVE on the XY, YZ and XZ axis planes are defined as principal planes, while the parallel planes opposite to the principal planes are classified as slave planes. A set of constraint equations in three directions are established on the unit nodes in the principal planes and slave planes, that is, periodic boundary conditions (such as Figure 4 shown);

[0093] In the X direction:

[0094] Each node of the main plane (x=0, yi, zi) and the node of the slave plane (x=Lx, yi, zi) must satisfy,

[0095] u(x=0,yi,zi)=u(x=Lx,yi,zi)+δx;

[0096] In the Y direction:

[0097] Each node of the main plane (xi, y=0, zi) and the node of the slave plane (xi, y=Ly, zi) must satisfy,

[0098] u(xi,y=0,zi)=u(xi,y=Ly,zi)+δy;

[0099] In the Z direction:

[0100] Each node of the main plane (xi, yi, z = 0) and the node of the slave plane (xi, yi, z = Lz) must satisfy,

[0101] u(xi, yi, z=0)=u(xi, yi, z=Lz)+δz;

[0102] S162. Select the same material to input into the analysis software. For example, the same material properties may be density, elastic modulus, and Poisson's ratio. In this embodiment, FormLab white resin is selected: density (ρ = 1.10 g / mm 3 ), Young’s modulus (Es = 2.51 GPa) and Poisson’s ratio (v = 0.23), all RVEs were batch processed and evaluated in ANSYS Mechanical APDL software to obtain the deformed RVEs (such as Figure 5 shown);

[0103] The deformation of representative volume units is calculated in batches. Since RVE can be regarded as orthogonal and isotropic, only the Z-axis direction needs to be calculated. The displacement is mainly calculated by applying equivalent stress in the Z-axis direction. The deformation of all representative volume units is calculated by the following formula (1):

[0104]

[0105] Among them, u z represents the displacement in the Z direction, δ z represents the deformation in the Z direction, represents the normal strain in the Z direction, RVE size is the length of RVE in the Z direction when it is not deformed (i.e., 18 mm in this embodiment); the calculations in the X and Y directions are consistent with those in the Z direction;

[0106] S17, calculate the elastic modulus of each lattice according to the deformation obtained in step S16; the calculation formula (2) is as follows:

[0107]

[0108] Among them, E z Indicates the elastic modulus in the Z direction, F z Indicates the load in the Z direction, A xy Indicates the area used for load, used to calculate stress σ z , δ z represents the deformation in the Z direction, l z It represents the length of the representative volume unit in the Z direction when it is not deformed and is used to calculate the strain ε z .

[0109] Since the relative density of the lattice model will be used in the subsequent formation and use of the lattice performance prediction model, it is necessary to calculate and predict the relative density of the lattice model; for new lattice structures, only the calculated relative density needs to be used in forming the lattice performance prediction model; and for existing lattice models, it is also necessary to quickly obtain the relative density of the corresponding lattice model. Here, a relative density prediction model is designed.

[0110] S20, the formation of the relative density prediction model mainly includes the following steps:

[0111] S21, obtaining the N sets of structural parameter sets in step S13 and the N lattice models in step S14, respectively measuring the volumes of the corresponding lattice models, setting the density of the used material, so as to calculate the relative density of the lattice model; the relative density RD is calculated as shown in formula (3):

[0112]

[0113] Among them, ρ lattice is the density of the lattice material (porous material); ρ solid The density of a solid material (usually a dense material without pores) is used as a reference.

[0114] For the rod-type lattice structure, there are 280 sets of structural parameter sets and 280 lattice models in this embodiment; the data obtained here are divided into two parts, one part is used for training the relative density prediction model, and the other part is used to verify the training results.

[0115] S22, using a multinomial regression model to train the data in step S21 to obtain a relative density prediction model, and optimizing the coefficients of the relative density prediction model by a least squares method;

[0116] The calculation formula (4) of the relative density prediction model is as follows:

[0117]

[0118] Where RD is the relative density, β0 is the intercept, and β i and β ij are the linear and quadratic coefficients, respectively, and X i and X j is a geometric parameter and ε is an error term.

[0119] The above lattice performance evaluation and relative density calculation have been completed; then it is necessary to establish the relationship between the lattice performance evaluation model, the relative density prediction model and the lattice performance prediction model.

[0120] S30, forming a lattice performance prediction model, mainly includes the following steps:

[0121] S31. Gather all the data to form a lattice performance evaluation model and a relative density prediction model and establish the relationship between the structural parameter set, the lattice model, the deformation, relative density, and elastic modulus of a representative volume unit.

[0122] S32, using the random forest model to train the data in step S31 to obtain a lattice performance prediction model; in this step, the random forest model is used to utilize its ability to handle complex nonlinear relationships and feature interactions. Formula (5) of the random forest model is:

[0123] E=RF(Z) (5)

[0124] Among them, Z is the input feature vector, including the structural parameters and relative density in the structural parameter set;

[0125] The training is performed using the structural parameter set, relative density, and elastic modulus. The random forest model consists of multiple decision trees, each of which is trained on different training samples and feature subsets. Finally, the accuracy and stability of the model are improved by integrating the prediction results of multiple decision trees. The formula (6) of the decision tree is:

[0126]

[0127] Among them, L is the number of leaf nodes in the decision tree, w i is the predicted value of the i-th leaf node, I(Z∈R i ) is an indicator function indicating whether Z falls into region R i ;

[0128] Based on formula (5) and formula (6), the lattice performance prediction model is finally obtained as follows:

[0129]

[0130] Among them, E RF (Z) is the predicted value of elastic modulus, m is the number of decision trees, T j (Z) is the predicted value of the jth decision tree.

[0131] At the same time, during the training and verification process, the corresponding structural parameters that affect the relative density and elastic modulus can also be given, and the corresponding sensitivity can be obtained to guide the user to make corresponding adjustments.

[0132] In order to verify the lattice performance prediction model after it is formed, all data input into the random forest model can be randomly divided into two parts, one part is used for model training, and the other part is used to verify the training results; the data used for model training can be 80% of all data, and the data used to verify the training results can be 20% of all data.

[0133] The lattice performance prediction model is obtained by training with 80% of the data, and then the structural parameters of the lattice in the remaining 20% ​​of the data are input into the relative density prediction model to obtain the predicted relative density. At the same time, the structural parameters and the predicted relative density are input into the lattice performance prediction model to obtain the predicted elastic modulus. Then the predicted relative density and the predicted elastic modulus are compared with the elastic modulus and the calculated relative density that have been calculated by the lattice performance evaluation model in the remaining 20% ​​of the data, so as to obtain the difference between them. Here, the cross-validation method is needed for verification. If the difference is too large, the hyperparameters of the machine learning model need to be adjusted. If the difference meets the requirements, the lattice performance prediction model is qualified. The results of the specific verification of the predicted relative density and the predicted elastic modulus are calculated using the mean absolute error (MAE), root mean square error (RMSE) and determination coefficient (R2 ), its formula (8), formula (9) and formula (10) are as follows:

[0134]

[0135] Among them, y i is the calculated value of relative density or elastic modulus, that is, calculated by a relative density prediction model or a lattice performance evaluation model; is the predicted value of relative density or elastic modulus, that is, it is predicted by the relative density prediction model or the lattice performance prediction model; m is the number of samples, is the predicted mean response, and the equation is

[0136] Based on the 280 structural parameter sets of the above-mentioned rod-like lattice structure, the data corresponding to 224 structural parameters are trained to obtain the lattice performance prediction model of the rod-like lattice structure, and the remaining 56 structural parameters are input into the relative density prediction model and the lattice performance prediction model to predict its relative density and elastic modulus to obtain the corresponding predicted values, and the predicted values ​​and the calculated values ​​corresponding to the 56 structural parameters are substituted into the above-mentioned formulas (8), (9) and (10), and the following calculation results are obtained:

[0137] MAE RMES <![CDATA[R 2 ]]> <![CDATA[Cross-validation R 2 Standard deviation]]> Relative density prediction 0.0073 0.011 0.829 0.065 Elastic modulus prediction 4.509 6.017 0.965 0.010

[0138] A polynomial regression model was used for relative density prediction, which has strong prediction ability. 2 It reaches 0.829, indicating that the prediction model predicts the relative density accurately and stably, and performs well on the test data with good fit. Similarly, the RMSE and MAE are 0.011 and 0.0073, respectively, confirming that the variance of the prediction results is small and acceptable because the RD is limited to between 0 and 1. The polynomial regression model is suitable for predicting continuous variables such as relative density, especially when the data show obvious nonlinear relationships. Its advantages are that it is simple and effective, and it can perform well even when the amount of data is small.

[0139] The random forest model is used to predict the elastic modulus, and the elastic modulus of the lattice is predicted by combining the predicted relative density and structural parameters, showing a highly accurate prediction ability, R 2 The relative density as an additional feature plays a key role in improving the accuracy of the predicted elastic modulus and greatly improves the accuracy of the prediction.

[0140] A lattice reverse optimization model is set up based on the trained relative density prediction model and lattice performance prediction model. Its purpose is to optimize the structural parameter set of the lattice structure under constraints through a genetic algorithm, so as to achieve customized design of the target structural parameters by inversely obtaining the elastic modulus. Through the iterative optimization of the genetic algorithm, the optimal solution in the complex design space can be effectively found.

[0141] S40, the formation of lattice inverse optimization model, such as Figure 6 As shown, the following steps are included:

[0142] S41. Select a lattice model that already exists in the lattice performance prediction model according to the requirements, and determine the domain value range of each structural parameter in the lattice model structure parameter set. If there is no requirement for the lattice model, it can also be matched by the system. If there is no requirement for the domain value range of each structural parameter, it can also be the default value. The default value here is the domain value range of the lattice performance evaluation model when the lattice structure is first input; here, it is also necessary to determine the target elastic modulus and relative density.

[0143] S42. Sampling is performed within the domain value range of each structural parameter, and corresponding structural parameter sets are composed of all different parameters, and multiple groups of structural parameter sets are obtained through sampling; the structural parameter set here can directly adopt the structural parameter set in the lattice performance evaluation model, or re-sample to obtain a new structural parameter set.

[0144] S43, inputting the structural parameters of multiple groups of structural parameter sets into the relative density prediction model to obtain multiple groups of relative densities, and then inputting the multiple groups of corresponding structural parameters and relative densities into the lattice performance prediction model to obtain the predicted elastic modulus; this step obtains the predicted elastic modulus and the corresponding relative density.

[0145] S44. The fitness function is used to evaluate the pros and cons of each structural parameter set, aiming to find the lattice structure with the minimum relative density under the expected customized performance requirements. The fitness function formula (11) is:

[0146]

[0147] Among them, V Individual is the structural parameter set, is the elastic modulus predicted by the lattice property prediction model, is the target elastic modulus, RD is the relative density, w1 and w2 are weight coefficients used to adjust the balance between target performance and relative density.

[0148] S45, using a roulette wheel selection or tournament selection method to select multiple groups of structural parameter sets according to fitness values; the fitness values ​​reflect the deviation between the lattice structure elastic modulus corresponding to each structural parameter set and the target elastic modulus;

[0149] S46. For the multiple groups of structure parameter sets in step S45, multiple groups of structure parameter sets are formed again by crossover operation and / or mutation operation for the structure parameters in each group of structure parameter sets.

[0150] S47, returning to iterative execution steps S43-S46, until the maximum number of iterations is reached or the fitness value converges, and terminating the operation, thereby minimizing the absolute deviation between the predicted elastic modulus and the target elastic modulus and minimizing the relative density.

[0151] For the above-mentioned lattice performance evaluation and prediction system, it can be used flexibly according to needs during use. There are mainly three ways of use:

[0152] The first one is that when there is no corresponding lattice structure in the lattice performance prediction model and the elastic modulus needs to be obtained, at this time, it is a forward design. First, the structural parameters of the lattice structure to be designed and the domain value range of the structural parameters need to be input into the lattice performance evaluation model. The lattice performance evaluation model outputs multiple sets of structural parameter sets and multiple lattice models to the relative density prediction model for training the lattice relative density prediction model. At the same time, the lattice performance evaluation model outputs the elastic modulus and the relative density prediction model outputs the relative density to the lattice performance prediction model for training the lattice performance prediction model of the lattice structure, and the relative density prediction model and the lattice performance prediction model of the lattice structure are obtained. Afterwards, the elastic modulus of the corresponding structural parameters can be given by the lattice performance prediction model, and the structural parameters with greater sensitivity can be adjusted according to the elastic modulus actually required until the corresponding elastic modulus meets the actual requirements.

[0153] The second type is when the corresponding lattice structure already exists in the lattice performance prediction model and the elastic modulus needs to be obtained. At this time, it is a forward design. First, the structural parameters of the lattice structure to be designed are directly input into the relative density prediction model and the lattice performance prediction model. The relative density prediction model outputs the predicted relative density and inputs it into the lattice performance prediction model together with the structural parameters. The lattice performance prediction model gives the elastic modulus of the corresponding structural parameters. The more sensitive structural parameters can be adjusted according to the elastic modulus actually required until the corresponding elastic modulus meets the actual needs.

[0154] The third type is that for the existing lattice structure in the lattice performance prediction model, there are special requirements for the elastic modulus and relative density, but there are no requirements for the lattice structure. At this time, for reverse design, it is necessary to use the trained relative density prediction model and lattice performance prediction model, and cooperate with the reverse optimization model using genetic algorithm. First, the target elastic modulus is put into the lattice reverse optimization model, and the lattice model is selected or matched by the system. When necessary, the domain value range of the structural parameters is input; the lattice reverse optimization model cooperates with the relative density prediction model and the lattice performance prediction model according to the genetic algorithm to finally obtain the optimal structural parameter set that meets the target elastic modulus and relative density.

[0155] In order to verify the effectiveness and advantages of this system, the traditional parameterized lattice design is used as a benchmark for comparative analysis, and the elastic modulus is analyzed, e.g. Figure 7 As shown, L defines the inner box size of the lattice unit, and D represents the diameter of the lattice pillar. At the same relative density, the elastic modulus of the lattice structure designed by the present system and the conventional lattice structure are shown. The lattice material designed by the present system shows a better upper limit of the elastic modulus under the same quality conditions, which indicates the improvement of material utilization and superior performance.

[0156] Based on the above system and method, four lattice materials with elastic modulus in the range of 30-35MPa and the lowest relative density were customized through forward design; the traditional bar-like lattice structure (BBC) was used as the standard for comparing mechanical properties, and the four customized lattice structures were marked as C1, C2, C3, and C4, respectively. Each lattice sample was produced twice using stereolithography (SLA) on the FormLab3 printer. Post-processing included cleaning the samples in 99.8% isopropyl alcohol with an ultrasonic cleaner for 10 minutes to eliminate any residual resin and ensure the cleanliness and integrity of the samples. Subsequently, they were cured in the FormLab UV curing machine and gradually heated to 60°C within 60 minutes. Finally, a 6×6×6 structural unit was selected for compression testing on the Sansi Zongheng universal testing machine; the specific data are shown in the following table:

[0157]

[0158]

[0159] The above table gives a detailed comparison between the traditional BCC lattice material and four customized lattice materials (C1, C2, C3, C4). The FormLab3 SLA printer captures the geometric features of the digital model very well; the relative density (RD) of all samples is strictly maintained within the target range of 0.15-0.16, and the elastic modulus (Es) indicator reveals the mechanical property enhancement achieved by the method proposed in this application. Specifically, C1 exhibits the highest elastic modulus at 11.27MPa, which is about 25.6% higher than the 8.97MPa of the traditional BCC lattice. C4 ranks behind with an elastic modulus 21.5% higher than the traditional lattice. C1 and C4 particularly show closely matched values ​​in parameters, revealing similar geometric features that affect their mechanical properties. This significant improvement emphasizes the advantage of lattice customization in improving material stiffness under compressive loads.

[0160] like Figure 8 Shown are the pressure-strain diagrams of BBC and four types of lattices. From the figure, it can be seen that the mechanical properties of the four optimized lattice structures are better than those of the traditional BBC lattice structure.

[0161] Analyze the parameters, relative density, and elastic modulus of the structural parameter set of this application to find out the parameters with higher sensitivity, so as to facilitate the adjustment of forward and reverse design; Fig. 9 As shown, there is a strong correlation between Minn and RD, while except for Mstrut, other variables also show high correlation with RD. In addition, there is no obvious relationship between the structural parameters; Fig.10 A similar trend was observed between the RD and the elastic modulus, and a strong correlation was found between the RD and the elastic modulus.

[0162] Based on the above system and method, four different lattice structures were customized through reverse design, with the target elastic modulus E target In the range of 80 to 120 MPa, while ensuring the lowest possible relative density. A 3×3×3 lattice unit was selected as the representative volume unit (RVE) for homogenization analysis; the customized target and reverse design parameters are shown in the following table:

[0163]

[0164]

[0165] In the above table, RD pred Represents the relative density predicted by the relative density prediction model, RD CAD Indicates the actual relative density of the lattice (obtained by calculation); E pred represents the elastic modulus predicted by the lattice performance prediction model, E sim Represents the actual elastic modulus of the lattice.

[0166] The accuracy of the reverse design is determined by the relative error (RE) formula, as shown in formula (12):

[0167]

[0168] Among them, V pred represents the predicted value, V actual Represents actual value.

[0169] like Fig.11 The predicted values ​​of relative density show variability according to the target value of elastic modulus. target Next, RD pred shows a small positive error, then at medium E target It turns negative at low values ​​and decreases again at higher values. target When RD is 80MPa, pred The error reached 2.25%, but these errors are within the acceptable range.

[0170] In terms of customized elastic modulus, E pred With E target The relative error between is small, indicating that the genetic algorithm is easy to converge. This accuracy demonstrates the ability of genetics to effectively navigate in the parameter space defined by the two-layer ML model (polynomial regression model and random forest model) to optimize the lattice design. sim and E pred The error between the two results shows that the prediction ability of this system is stable, but it can be used as a reference because the fluctuation range is from 0.75% to 8.55%. pred At higher E target The error is larger as E target The increase gradually decreases and at lower E target It is noteworthy that the deviation trend shows a high consistency with the prediction errors of elastic modulus and relative density. pred The error increases, E pred The error is also magnified, which is consistent with Fig.12 The feature importance analysis results shown are consistent. The relative density error of polynomial regression can further expand the elastic modulus error of random forest regression. The four designed lattice materials all meet or exceed the target mechanical properties, thus verifying the predictive accuracy and practical applicability of our design method.

[0171] In terms of the forward design process, a two-layer machine learning model is proposed. The first layer model is used to predict the relative density with geometric parameters as external features to compensate for the accuracy and robustness of the second layer model. Polynomial regression captures the complex interaction between geometric parameters, thus predicting the relative density well; the second layer model is used to predict the elastic modulus; it is worth noting that the prediction of the elastic modulus shows significant adaptability (RMES = 6.017, R 2 =0.965). Feature importance analysis shows that relative density highlights consistency and relative density as an external feature can significantly improve the predictability of this system.

[0172] In the reverse design stage, a genetic algorithm is used to search for lattice materials with the required properties and low density to improve material utilization. The imposed polynomial constraints show that although it ensures a certain physical consistency. Compared with conventional parameter lattice materials, this method not only expands the performance space, but also optimizes the upper limit of mechanical properties.

[0173] The integration of machine learning not only helps to better understand these complexities, but also enhances the ability to effectively predict and optimize material properties. Genetic algorithms facilitate the inverse design of lattice materials. In addition, this approach reduces reliance on trial and error, advancing a more efficient and scientific design process.

[0174] It should be emphasized that the above are only preferred embodiments of the present invention and do not limit the present invention in any form. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A method for forming a lattice performance evaluation and prediction system, characterized in that: The lattice performance evaluation and prediction system includes a lattice performance evaluation model, a relative density prediction model and a lattice performance prediction model. The steps of the formation method are: S10, forming a lattice performance evaluation model, the lattice performance evaluation model is composed of the following steps; S11, according to the specific structure of the lattice to be designed, all structural parameters affecting the lattice structure are obtained to form a structural parameter set; S12. Determine the domain value range of each structural parameter according to actual needs; S13, sampling is performed within the domain value range of each structural parameter, all different parameters form a corresponding structural parameter set, and N groups of structural parameter sets are obtained through sampling; S14, modeling the N sets of structural parameter sets in 3D software to form lattice models of N smooth subdivision surfaces; S15, obtaining representative volume units for each lattice model; S16. Establishing periodic boundary conditions for each representative volume unit and setting the same material properties, applying equivalent stress, and obtaining the deformation of the corresponding representative volume unit; S17, calculating the elastic modulus of each lattice according to the deformation and equivalent stress obtained in step S16; S20, the formation of a relative density prediction model, the relative density prediction model is formed by the following steps; S21, obtaining N sets of structural parameter sets in step S13 and N lattice models in step S14, setting material density, and calculating the relative density of each lattice model; S22, using a multinomial regression model to train the data in step S21 to obtain a relative density prediction model, and optimizing the coefficients of the relative density prediction model by a least squares method; S30, forming a lattice performance prediction model, the lattice performance prediction model is formed by the following steps; S31, gathering all data forming a lattice performance evaluation model and a relative density prediction model and establishing a relationship between a structure parameter set, a lattice model, deformation of a representative volume unit, relative density, and elastic modulus; S32. Use the random forest model to train the data in step S31 to obtain a lattice performance prediction model.

2. The method for forming a lattice performance evaluation and prediction system according to claim 1, characterized in that: The steps of executing step S16 are: S161, the surfaces of the representative volume unit on the XY, YZ and XZ axis planes are defined as principal planes, and the parallel planes opposite to the principal planes are classified as slave planes, and a set of constraint equations in three directions are established on the unit nodes in the principal planes and the slave planes; S162. Select the same material input analysis software, batch calculate the deformation of representative volume units, and calculate the deformation of all representative units separately using the following formula: Among them, u z represents the displacement in the Z direction, δ z represents the deformation in the Z direction, represents the normal strain in the Z direction, RVE size It is the length of the representative volume unit in the Z direction when it is not deformed; the calculations in the X and Y directions are consistent with the Z direction.

3. The method for forming a lattice performance evaluation and prediction system according to claim 1, characterized in that: The calculation formula of the elastic modulus in step S17 is: Among them, E z Indicates the elastic modulus in the Z direction, F z Indicates the load in the Z direction, A xy Indicates the area used for load, used to calculate stress σ z , δ z represents the deformation in the Z direction, l z It represents the length of the representative volume unit in the Z direction when it is not deformed and is used to calculate the strain ε z .

4. The method for forming a lattice performance evaluation and prediction system according to claim 1, characterized in that: In step S22, the relative density prediction model is: Where RD is the relative density, β0 is the intercept, and β i and β ij are the linear and quadratic coefficients, respectively, and X i and X j is a geometric parameter and ε is an error term.

5. The method for forming a lattice performance evaluation and prediction system according to claim 4, characterized in that: The data in step S21 is divided into two parts, one part is used for model training, and the other part is used to verify the training results.

6. The method for forming a lattice performance evaluation and prediction system according to claim 1, characterized in that: In step S32, the lattice performance prediction model is: Among them, E RF (Z) is the predicted value of elastic modulus, m is the number of decision trees, T j (Z) is the predicted value of the jth decision tree; The calculation formula of the decision tree is: Among them, L is the number of leaf nodes in the decision tree, w i is the predicted value of the i-th leaf node, I(Z∈R i ) is an indicator function indicating whether Z falls into region R i .

7. The method for forming a lattice performance evaluation and prediction system according to claim 1, characterized in that: In step S32, all data input into the random forest model are randomly divided into two parts, one part is used for model training, and the other part is used to verify the training results; 80% of the data is used for model training, and 20% of the data is used for verifying the training results.

8. The method for forming a lattice performance evaluation and prediction system according to claim 6, characterized in that: By using the mean absolute error MAE, root mean square error RMSE and determination coefficient R 2 To verify the predicted elastic modulus results, the formula is as follows, Among them, y i is the calculated value of relative density or elastic modulus, is the predicted value of relative density or elastic modulus, m is the number of samples, is the predicted mean response.

9. The method for forming a lattice performance evaluation and prediction system according to claim 1, characterized in that: A lattice inverse optimization model is set based on the lattice performance prediction model. The optimization method of the lattice inverse optimization model is: S41, determining the domain value range of each structural parameter in the structural parameter set, and determining the elastic modulus and relative density of the target; S42, sampling is performed within the domain value range of each structural parameter, all different parameters form a corresponding structural parameter set, and multiple groups of structural parameter sets are obtained through sampling; S43, inputting the structural parameters of the multiple groups of structural parameter sets into the lattice performance prediction model and the relative density prediction model to obtain the predicted elastic modulus and relative density corresponding to each structural parameter set; S44. Evaluate the quality of each structural parameter set according to the fitness function. The fitness function is: Among them, V Individual is the structural parameter set, is the elastic modulus predicted by the lattice property prediction model, is the target elastic modulus, RD is the relative density, w1 and w2 are weight coefficients used to adjust the balance between target performance and relative density; S45, selecting multiple sets of structural parameter sets according to fitness values ​​using a roulette wheel selection or a tournament selection method; S46, for the multiple sets of structural parameter sets, the structural parameters are subjected to crossover operation and / or mutation operation to form multiple new sets of structural parameter sets; S47, returning to iterative execution steps S43-S46, until the maximum number of iterations is reached or the fitness value converges, and terminating the operation, so that the absolute deviation between the predicted elastic modulus and the target elastic modulus is minimized and the relative density is minimized.

10. The method for forming a lattice performance evaluation and prediction system according to claim 1, characterized in that: The lattice model is a rod-type lattice structure, and its structural parameter set is {Minn, Mout, Mstrut, Msmooth, Tcube}, where Minn is the size of the internal nodes of the lattice unit, Mout is the size of the external nodes of the lattice unit, Mstrut is a parameter that describes the radius size of the lattice unit pillar, Msmooth is a parameter that determines the smoothness of the lattice pillar, and Tcube is a parameter that determines the size of the square grid formed by the internal nodes of the lattice unit.

11. The method for forming a lattice performance evaluation and prediction system according to claim 10, characterized in that: In step S14, the modeling method of the lattice model is to first create a rough polygonal mesh surface model, in which the parameters affecting the polygonal mesh surface model correspond one to one with the structural parameters, and then form lattice units according to the specific structural parameters and based on the subdivision surface modeling method, and finally form a lattice structure composed of multiple lattice units to form a lattice model.

12. The method for forming a lattice performance evaluation and prediction system according to claim 1, characterized in that: In step S13, sampling is performed by using the Latin hypercube sampling method.

13. A method for using the lattice performance evaluation and prediction system of claim 1, characterized in that: Firstly, the structural parameters of the lattice structure and the domain value range of the structural parameters are input into the lattice performance evaluation model, and the lattice performance evaluation model outputs multiple groups of structural parameter sets and multiple lattice models to the relative density prediction model for training the lattice relative density prediction model. At the same time, the lattice performance evaluation model outputs the elastic modulus and the relative density prediction model outputs the relative density to the lattice performance prediction model for training the lattice performance prediction model of the lattice structure, and the relative density prediction model and the lattice performance prediction model of the lattice structure are obtained. Afterwards, the elastic modulus of the corresponding structural parameters can be given through the lattice performance prediction model, and the structural parameters with greater sensitivity can be adjusted according to the elastic modulus actually required until the corresponding elastic modulus meets the actual requirements.

14. A method for using the lattice performance evaluation and prediction system of claim 1, characterized in that: First, the structural parameters of the lattice structure to be designed are directly input into the relative density prediction model and the lattice performance prediction model. The relative density prediction model outputs the predicted relative density and inputs it into the lattice performance prediction model together with the structural parameters. The lattice performance prediction model gives the elastic modulus of the corresponding structural parameters. The structural parameters with greater sensitivity can be adjusted according to the elastic modulus actually required until the corresponding elastic modulus meets the actual requirements.

15. A method for using the lattice performance evaluation and prediction system of claim 9, characterized in that: First, the target elastic modulus is input into the lattice inverse optimization model, and the lattice model is selected or matched by the system; the lattice inverse optimization model finally obtains the optimal structural parameter set that meets the target elastic modulus and relative density based on the genetic algorithm in conjunction with the relative density prediction model and the lattice performance prediction model.

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