Metamaterial design method based on density constraint and interpretable ai

Abstract

The application discloses a metamaterial design method based on density constraint and explainable AI, and relates to the technical field of additive manufacturing; geometric data of the metamaterial is acquired to generate a three-dimensional model, a topographic parameter extraction script is run to obtain a topographic parameter vector, and a mechanical property vector of the metamaterial is acquired, a density constraint condition is set according to the metamaterial, a candidate enhancement strategy is generated for a training set composed of the topographic parameter vector and the mechanical property vector, a consistency index is calculated according to the topographic parameter vector, and an optimal enhancement strategy is selected, an optimal model is obtained through model selection based on an integrated learning model family, global and individual explanations are performed through SHAP, and key topographic parameter features are identified, and the action trend and sensitive interval of the key topographic parameter features on the target mechanical property vector are identified; the metamaterial design method based on the density constraint and the explainable AI is used, the reliability of model prediction is enhanced, and the cost of traditional test iteration and parameter trial and error is significantly reduced.

Description

Technical Field

[0001] This invention relates to the field of additive manufacturing technology, and in particular to a metamaterial design method based on density constraints and interpretable AI. Background Technology

[0002] Lattice metamaterials (including three-period minimum surface TPMS and bar lattices) have shown the potential for "material-structure integration" in fields such as lightweight load-bearing, energy absorption and protection, heat dissipation / mass transfer and biomedical applications due to their designable geometry-topology configuration and adjustable relative density. Their macroscopic mechanical response depends not only on the matrix material, but also on structural parameters such as the relative density of the configuration geometry. Especially under additive manufacturing conditions, the detailed geometry such as thin walls, nodes and transition zones directly determine the local buckling and failure modes, so that even if the substrate is the same, structural components with different geometry-topologies may exhibit significant anisotropy and multimodal instability.

[0003] From the perspective of design and modeling methods, traditional empirical parameter tuning or pure black-box machine learning have the following typical shortcomings:

[0004] Density heterogeneity: The relative density differences between different samples often have a greater influence on the mechanical response than geometric details. If comparisons and models are not performed under the premise of isodense or controlled density bandwidth, false superiority or incomparable cross-configuration conclusions can easily be generated, which reduces the engineering usability.

[0005] Unexplainability: While black-box prediction may improve scores, it lacks information on "which morphological factors, within what threshold range, and in what direction" are dominant. , , The chain of evidence, among which, Indicates the elastic modulus. For yield strength, This means by 0.2. Yield strength obtained by the offset method The specific energy absorption value is insufficient to support design review, parameter finalization, and quality traceability.

[0006] Insufficient cross-configuration migration: TPMS is based on curvature field and surface metric, while bar lattice is based on directional bar segment statistics, nodal loops and nodal curvature. The two have different parameter semantics and scale characteristics, and lack a unified design paradigm that takes into account comparability and interpretability at the same time.

[0007] Lack of data consistency: Directly using conventional data augmentation under small sample conditions, without implementing consistency constraints on marginal distribution and related structures, can easily introduce distribution shifts, disrupt the joint distribution of relative density and morphological parameters, and thus weaken the model's stability and interpretability. Summary of the Invention

[0008] The purpose of this invention is to provide a metamaterial design method based on density constraints and interpretable AI. This method not only ensures the comparability and interpretability of different types of lattices under equal density conditions, but also ensures the reliability of model predictions through consistency enhancement and verification closed loop. It significantly reduces the cost of traditional experimental iteration and parameter trial and error, and provides a directly applicable solution for lattice configuration design and performance prediction in the field of additive manufacturing, with broad prospects for industrial application.

[0009] To achieve the above objectives, this invention provides a metamaterial design method based on density constraints and interpretable AI, comprising the following steps:

[0010] S1. Obtain the geometric data of metamaterials to generate a 3D model;

[0011] S2. Run the topography parameter extraction script from the 3D model generated in S1 to obtain the topography parameter vector. ;

[0012] S3. Obtain the mechanical property vector by performing mechanical measurements on the metamaterial of S1. ;

[0013] S4. Set density constraint conditions based on the metamaterial in S1;

[0014] After S5 and S4 are completed, the shape parameter vector is... and mechanical property vector The training set is used to generate candidate augmentation strategies;

[0015] S6. Based on the morphological parameter vector Calculate marginal consistency and relevant consistency indices and combine them with S5 to select the optimal enhancement strategy;

[0016] After S7 and S6 are completed, the optimal model is obtained by selecting models based on the family of ensemble learning models.

[0017] S8. Based on the optimal model in S7, the global and individual interpretations are performed using the Shapley and SHAP interpretation methods to identify key morphological parameters and their influence trends and sensitive ranges on the target mechanical performance vector.

[0018] Preferably, the metamaterial includes a three-period minimum surface TPMS lattice and a bar lattice. When the metamaterial is a TPMS lattice, the morphology parameter vector... Includes the total surface area (Area), specific surface area (SSA), first principal moment of inertia (I1InertiaI1), second principal moment of inertia (I2InertiaI2), third principal moment of inertia (I3InertiaI3), and the weighted average of the mean curvature (H). mean Mean curvature standard deviation H std Mean curvature median H medMean curvature interquartile range H iqr Gaussian curvature weighted mean K mean Gaussian curvature standard deviation K std Median Gaussian curvature K med Gaussian curvature interquartile range K iqr Average connectivity CN mean Connectivity standard deviation CN std Degree Entropy;

[0019] When the metamaterial is a bar lattice Including SSA, X direction support segment number X SC , Number of pillar segments in Y direction Y SC , Number of pillar segments in Z direction Z SC Number of inclined support segments SC Midpoint distribution standard deviation MidX in the X direction Std Midpoint distribution standard deviation in the Y direction (MidY) Std Midpoint distribution standard deviation in the Z direction (MidZ) Std Average connectivity CN mean Connectivity standard deviation CN std Euler's average number of loops per cell PC Mean curvature of nodes Cur Node curvature standard deviation Std Cur Node mean Gaussian curvature Mean Gau Node Gaussian curvature standard deviation Std Gau .

[0020] Preferably, the mechanical property vector of S3 ,in, Indicates the elastic modulus. For yield strength, This means by 0.2. Yield strength obtained by the offset method The specific energy absorption value is calculated using the formula for integrating the stress-strain curve over the strain interval before the peak. , Indicates engineering strain. This represents the maximum effective strain of a material before it reaches its peak stress.

[0021] Preferably, the density constraints of S4 include equal density, bandwidth density, and relative density RD;

[0022] To ensure that different metamaterial samples can be compared and analyzed and model trained under the same relative density (RD) conditions. To achieve isodensity constraints, where The target relative density constant is a pre-selected value used to represent the nominal relative density level of each metamaterial sample under isodense conditions.

[0023] To impose restrictions on the density distribution, only data points or regions with density falling within a certain interval are considered. Implement bandwidth density constraints and perform weighted sampling, where This is the minimum relative density value accepted for bandwidth density comparison, corresponding to the lowest permissible relative density for TPMS and rod-lattice metamaterials under requirements of manufacturing precision, minimum geometric wall thickness, and mechanical stability. The maximum relative density value accepted for bandwidth density comparison corresponds to the highest relative density allowed under equivalent volume conditions for metamaterials of the TPMS lattice and rod lattice types.

[0024] The relative density RD is a fixed value, that is Or located in the interval Internally, relative density RD is used as the anchor parameter to perform screening, normalization and weighting processing on the sample data to ensure the comparability and consistency of different metamaterials or batches of samples on the density scale.

[0025] Preferably, the quality control content for relative density RD as the anchor point parameter is as follows:

[0026] Based on the criterion of high correlation with relative density RD and non-excessive collinearity, a pairing set of relative density RD and morphological parameters is selected. The redundancy removal criterion between morphological parameters is set as follows: 0.98, of which, Represents any two topographic parameters and The Pearson correlation coefficient between them 0.98 indicates that the absolute value of the correlation coefficient between the two morphological parameters does not exceed 0.98;

[0027] For each pair of relative density-morphology parameters, the Pearson correlation coefficient was calculated. and ,in, This represents the Pearson correlation coefficient between the relative density RD in the original training dataset and the morphological parameter under the current RD stratification conditions. This represents the Pearson correlation coefficient of the corresponding RD-morphology parameter pairs in the augmented dataset. For statistical equivalence testing, the above correlation coefficient is... The transformation maps to an approximately normal distribution space and is used to measure the statistical bias of the structural differences between the augmented and original data; the difference is... :

[0028] ;

[0029] in The inverse hyperbolic tangent function is used to map the Pearson correlation coefficient to... The space is made to approximately follow a standard normal distribution in order to perform statistical equivalence tests, when The 95% confidence upper bound is satisfied. At that time, among them For tolerance zone and If so, it is determined that the correlation structure between the augmented data and the original data at the relative density anchor point is statistically equivalent;

[0030] If it exceeds the tolerance zone If this occurs, it indicates that the enhancement process has disrupted the natural correlation structure between the relative density and morphology parameter pairings. The enhancement strategy should be adjusted or the perturbation amplitude reduced until the data distribution consistency is restored.

[0031] Preferably, the candidate enhancement strategies for S5 include a dithering and hybrid enhancement strategy and a connection function enhancement strategy based on relative density conditionalization, the details of which are as follows:

[0032] The jitter and blending enhancement strategy, targeting continuous topographic parameters and mechanical performance indicators, performs the following random perturbation and sample blending operations on the topographic parameter vector. and mechanical property vector Gaussian perturbations were applied respectively to obtain and As shown below:

[0033] ;

[0034] ;

[0035] in, for Samples after applying Gaussian perturbation The symbol for element-wise multiplication. Original sample The amplitude of the disturbance and , Mechanical property vector Samples after applying Gaussian perturbation It follows a normal distribution. Let represent the random perturbation factor applied to the topographic parameter vector , which follows a zero-mean normal distribution. To represent the vector of mechanical properties applied The random disturbance factor follows a zero-mean normal distribution. Original sample The amplitude of the disturbance and The relative density RD remains frozen during this stage to ensure that the enhanced samples are within the same density anchor layer;

[0036] Select any two pairs of samples after applying Gaussian perturbation , The two mixed samples are obtained by performing linear mixing based on the beta distribution. , The details are as follows:

[0037] ;

[0038] ;

[0039] in, for and The mixed sample, for and Mixed samples, mixing coefficient The random mixing coefficients are in the interval 0 to 1, used to linearly weight the morphological parameter vectors and mechanical performance indices of any two sets of samples. Obtain the parameter as of Distribution, its probability density function for: ,in, for function; To control the distribution shape parameter of the mixing degree, when When the value is in the range of 0.2 to 0.6, the generated The values ​​tend to be closer to 0 or 1, making the mixed samples closer to one of the original samples, thereby enhancing the differences between samples and avoiding over-smoothing;

[0040] Based on a relative density-conditionalized connectivity function enhancement strategy, under equal density or bandwidth density constraints, connectivity function enhancement is performed on continuous features using 4–6 binning layers based on quantiles as conditional variables, with each topographic parameter vector as the conditional variable. The process of performing normal join function mapping is as follows:

[0041] ;

[0042] in, It is the standard normal distribution function. It is the inverse function of the standard normal distribution. It is the empirical distribution function;

[0043] The correlation matrix of Gaussian connection functions between fitted features within each density sublayer is calculated. And perform multivariate normal sampling to generate new enhanced morphology parameter samples. and Then, an inverse transformation is performed to obtain the reconstructed topographic parameter vector. and For discrete parameters or parameters with narrow numerical ranges, bootstrap sampling or adding small perturbations can be used to enhance the samples. The settings for adding small perturbations are as follows: and The perturbation amplitude is used to introduce finite randomness to prevent complete duplication of augmented samples while ensuring the physical feasibility of the parameters.

[0044] Preferably, in S6, the marginal consistency index and the relevant consistency index are the judgment thresholds for selecting the optimal enhancement strategy, and the marginal consistency index is... , ,in Tested for Kolmogorov–Smirnov The value is used to measure whether the marginal distributions of augmented data and original data on the same morphological parameter are statistically consistent; The normalized result of the first Wasserstein distance is used to measure the degree of distributional offset between the augmented data and the original data on the same topographic parameter, and is a relevant consistency index. The absolute difference between the Pearson correlation coefficients of relative density RD and morphology parameters before and after data augmentation is given. The threshold requirements for all indicators are as follows:

[0045] Must meet , Must meet , Must meet ;

[0046] Preferably, the process of selecting the optimal enhancement strategy in S6 is as follows:

[0047] The optimal strategy is selected from two categories: jitter and hybrid enhancement strategy and connection function enhancement strategy based on relative density conditionalization. The selection criterion is whether a threshold is met. , , ;

[0048] When the threshold is detected , , If all requirements are met, continue executing the dithering and hybrid enhancement strategy; when a threshold is detected... , , If 1 to 3 of the requirements are not met, the gatekeeper is triggered to back off, and the connection function enhancement strategy based on relative density conditionalization is switched first and the layering and perturbation amplitude are refined.

[0049] Preferably, the model family of S7 includes CatBoost, LightGBM, XGBoost and Random Forest. All models are used for training and K-fold cross-validation and early stopping are employed. The optimal model is selected based on the root mean square error (RMSE).

[0050] Preferably, the specific process of S8 is as follows:

[0051] S81. Perform SHAP global interpretation based on the optimal model, and use the Shapley sum interpretation method (SHAP) to calculate the vector of target mechanical properties for each topographic parameter. The absolute mean of Shapley's contribution values As a measure of the global importance of this morphological parameter, a SHAP global importance graph is generated, sorted from largest to smallest contribution, and the final set of key morphological parameters is determined based on the principle of relevance redundancy removal.

[0052] S82. Based on the median prediction samples, perform SHAP individual interpretation, select typical samples whose prediction results are near the median of the statistical distribution of the test set, and interpret them through SHAP force plots or by analyzing their key morphological parameters. , and The positive or negative contribution can be used to obtain a quantifiable mapping relationship;

[0053] S83. Combining the global and individual interpretation results of SHAP, the contribution direction, contribution magnitude and sensitive range of the morphological parameters in different value ranges are comprehensively determined to obtain the main trend of the key morphological parameters on the above mechanical properties and their variation range, and based on this, parameter action rules that can be used for engineering design are formed.

[0054] Therefore, the metamaterial design method based on density constraints and interpretable AI described above has the following advantages compared with the prior art:

[0055] 1. The design method of this application has better density fairness, and cross-configuration comparison is performed under equal density or bandwidth-controlled conditions to avoid false superiority caused by density differences;

[0056] 2. This application has stronger controllability and interpretability, outputting an auditable chain of evidence for key morphological factors, thresholds, intervals, and influence directions, supporting targeted design and quality traceability;

[0057] 3. The design method of this application uses statistical and structural consistency constraints to enhance data, and incorporates backoff and directional contraction mechanisms, which effectively enhances the robustness of the model, threshold-triggered updates, and improves the model's continuous generalization ability.

[0058] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0059] Figure 1 This is an overall flowchart of a metamaterial design method based on density constraints and interpretable AI according to the present invention;

[0060] Figure 2 This is a TPMS geometric model diagram of a metamaterial design method based on density constraints and interpretable AI according to the present invention;

[0061] Figure 3 This is a schematic diagram of the relative density anchor point control of a metamaterial design method based on density constraints and interpretable AI according to the present invention.

[0062] Figure 4 This is a graph showing the machine learning model fitting and residual distribution results of a Diamond-sheet lattice sample for a metamaterial design method based on density constraints and interpretable AI, as described in this invention.

[0063] Figure 5 This is a SHAP global analysis diagram of a metamaterial design method based on density constraints and interpretable AI according to the present invention;

[0064] Figure 6 This is the SHAP median sample individual interpretation diagram of a metamaterial design method based on density constraints and interpretable AI according to the present invention. Detailed Implementation

[0065] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the product of this invention is usually placed when in use. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0066] Example

[0067] like Figure 1 As shown, the present invention provides a metamaterial design method based on density constraints and interpretable AI, comprising the following steps:

[0068] S1. Obtain the geometric data of metamaterials to generate a 3D model;

[0069] Metamaterials include three-period minimum surface TPMS lattices and bar lattices. When the metamaterial is a TPMS lattice, the morphology parameter vector... Includes the total surface area (Area), specific surface area (SSA), first principal moment of inertia (I1InertiaI1), second principal moment of inertia (I2InertiaI2), third principal moment of inertia (I3InertiaI3), and the weighted average of the mean curvature (H). mean Mean curvature standard deviation H std Mean curvature median H med Mean curvature interquartile range H iqr Gaussian curvature weighted mean K mean Gaussian curvature standard deviation K std Median Gaussian curvature K med Gaussian curvature interquartile range K iqr Average connectivity CN mean Connectivity standard deviation CN std Degree Entropy;

[0070] When the metamaterial is a bar lattice Including SSA, X direction support segment number X SC , Number of pillar segments in Y direction Y SC , Number of pillar segments in Z direction Z SC Number of inclined support segments SC Midpoint distribution standard deviation MidX in the X direction Std Midpoint distribution standard deviation in the Y direction (MidY) Std Midpoint distribution standard deviation in the Z direction (MidZ) Std Average connectivity CN mean Connectivity standard deviation CN std Euler's average number of loops per cell PC Mean curvature of nodes Cur Node curvature standard deviation Std Cur Node mean Gaussian curvature Mean Gau Node Gaussian curvature standard deviation Std Gau ;

[0071] S2. Run the topography parameter extraction script from the 3D model generated in S1 to obtain the topography parameter vector. ;

[0072] S3. Obtain the mechanical property vector by performing mechanical measurements on the metamaterial of S1. ;

[0073] Mechanical performance vector ,in, Indicates the elastic modulus. For yield strength, This means by 0.2. Yield strength obtained by the offset method The specific energy absorption value is calculated using the formula for integrating the stress-strain curve over the strain interval before the peak. , Indicates engineering strain. This represents the maximum effective strain of the material before it reaches peak stress.

[0074] S4. Set density constraint conditions based on the metamaterial in S1;

[0075] like Figure 3 As shown, density constraints include isodensity, bandwidth density, and relative density RD;

[0076] To ensure that different metamaterial samples can be compared and analyzed and model trained under the same relative density (RD) conditions. To achieve isodensity constraints, where The target relative density constant is a pre-selected value used to represent the nominal relative density level of each metamaterial sample under isodense conditions.

[0077] To impose restrictions on the density distribution, only data points or regions with density falling within a certain interval are considered. Implement bandwidth density constraints and perform weighted sampling, where This is the minimum relative density value accepted for bandwidth density comparison, corresponding to the lowest permissible relative density for TPMS and rod-lattice metamaterials under requirements of manufacturing precision, minimum geometric wall thickness, and mechanical stability. The maximum relative density value accepted for bandwidth density comparison corresponds to the highest relative density allowed under equivalent volume conditions for metamaterials of the TPMS lattice and rod lattice types.

[0078] The relative density RD is a fixed value, that is Or located in the interval Internally, relative density RD is used as the anchor parameter to perform screening, normalization and weighting processing on the sample data to ensure the comparability and consistency of different metamaterials or batches of samples on the density scale.

[0079] The quality control measures for relative density RD as an anchor point parameter are as follows:

[0080] Based on the criterion of high correlation with relative density RD and non-excessive collinearity, a pairing set of relative density RD and morphological parameters is selected. The redundancy removal criterion between morphological parameters is set as follows: 0.98, of which, Represents any two topographic parameters and The Pearson correlation coefficient between them 0.98 indicates that the absolute value of the correlation coefficient between the two morphological parameters does not exceed 0.98;

[0081] For each pair of relative density-morphology parameters, the Pearson correlation coefficient was calculated. and ,in, This represents the Pearson correlation coefficient between the relative density RD in the original training dataset and the morphological parameter under the current RD stratification conditions. This represents the Pearson correlation coefficient of the corresponding RD-morphology parameter pairs in the augmented dataset. For statistical equivalence testing, the above correlation coefficient is... The transformation maps to an approximately normal distribution space and is used to measure the statistical bias of the structural differences between the augmented and original data; the difference is... :

[0082] ;

[0083] in The inverse hyperbolic tangent function is used to map the Pearson correlation coefficient to... The space is made to approximately follow a standard normal distribution in order to perform statistical equivalence tests, when The 95% confidence upper bound is satisfied. At that time, among them For tolerance zone and If so, it is determined that the correlation structure between the augmented data and the original data at the relative density anchor point is statistically equivalent;

[0084] If it exceeds the tolerance zone If this indicates that the enhancement process has disrupted the natural correlation structure between the relative density and morphology parameter pairings, the enhancement strategy should be adjusted or the perturbation amplitude reduced until the data distribution consistency is restored.

[0085] After S5 and S4 are completed, the shape parameter vector is... and mechanical property vector The training set is used to generate candidate augmentation strategies;

[0086] Candidate enhancement strategies include dithering and hybrid enhancement strategies and connection function enhancement strategies based on relative density conditionalization, the details of which are as follows:

[0087] The jitter and blending enhancement strategy, targeting continuous topographic parameters and mechanical performance indicators, performs the following random perturbation and sample blending operations on the topographic parameter vector. and mechanical property vector Gaussian perturbations were applied respectively to obtain and As shown below:

[0088] ;

[0089] ;

[0090] in, for Samples after applying Gaussian perturbation The symbol for element-wise multiplication. Original sample The amplitude of the disturbance and , Mechanical property vector Samples after applying Gaussian perturbation It follows a normal distribution. Let represent the random perturbation factor applied to the topographic parameter vector , which follows a zero-mean normal distribution. To represent the vector of mechanical properties applied The random disturbance factor follows a zero-mean normal distribution. Original sample The amplitude of the disturbance and The relative density RD remains frozen during this stage to ensure that the enhanced samples are within the same density anchor layer;

[0091] Select any two pairs of samples after applying Gaussian perturbation , The two mixed samples are obtained by performing linear mixing based on the beta distribution. , The details are as follows:

[0092] ;

[0093] ;

[0094] in, for and The mixed sample, for and Mixed samples, mixing coefficient The random mixing coefficients are in the interval 0 to 1, used to linearly weight the morphological parameter vectors and mechanical performance indices of any two sets of samples. Obtain the parameter as of Distribution, its probability density function for: ,in, for function; To control the distribution shape parameter of the mixing degree, when When the value is in the range of 0.2 to 0.6, the generated The values ​​tend to be closer to 0 or 1, making the mixed samples closer to one of the original samples, thereby enhancing the differences between samples and avoiding over-smoothing;

[0095] Based on a relative density-conditionalized connectivity function enhancement strategy, under equal density or bandwidth density constraints, connectivity function enhancement is performed on continuous features using 4–6 binning layers based on quantiles as conditional variables, with each topographic parameter vector as the conditional variable. The process of performing normal join function mapping is as follows:

[0096] ;

[0097] in, It is the standard normal distribution function. It is the inverse function of the standard normal distribution. It is the empirical distribution function;

[0098] The correlation matrix of Gaussian connection functions between fitted features within each density sublayer is calculated. And perform multivariate normal sampling to generate new enhanced morphology parameter samples. and Then, an inverse transformation is performed to obtain the reconstructed topographic parameter vector. and For discrete parameters or parameters with narrow numerical ranges, bootstrap sampling or adding small perturbations can be used to enhance the samples. The settings for adding small perturbations are as follows: and The perturbation amplitude is used to introduce finite randomness to prevent complete duplication of augmented samples while ensuring the physical feasibility of the parameters.

[0099] S6. Based on the morphological parameter vector Calculate marginal consistency and relevant consistency indices and combine them with S5 to select the optimal enhancement strategy;

[0100] Marginal consistency index and relevant consistency index are the judgment thresholds for selecting the optimal enhancement strategy. The marginal consistency index is... (Kolmogorov-Smirnov Test), (Weighted Normalization, where) Tested for Kolmogorov–Smirnov The value is used to measure whether the marginal distributions of augmented data and original data on the same morphological parameter are statistically consistent; The normalized result of the first Wasserstein distance is used to measure the degree of distributional offset between the augmented data and the original data on the same topographic parameter. Weighted normalization and related consistency indices are also included. The absolute difference between the Pearson correlation coefficients of relative density RD and morphology parameters before and after data augmentation is given. The threshold requirements for all indicators are as follows:

[0101] Must meet , Must meet , Must meet ;

[0102] The process of selecting the optimal enhancement strategy is as follows:

[0103] The optimal strategy is selected from two categories: jitter and hybrid enhancement strategy and connection function enhancement strategy based on relative density conditionalization. The selection criterion is whether a threshold is met. , , ;

[0104] When the threshold is detected , , If all requirements are met, continue executing the dithering and hybrid enhancement strategy; when a threshold is detected... , , If 1 to 3 of the requirements are not met, the gatekeeper is triggered to back off, and the connection function enhancement strategy based on relative density conditionalization is switched first and the layering and perturbation amplitude are refined.

[0105] After S7 and S6 are completed, the optimal model is obtained by selecting models based on the family of ensemble learning models.

[0106] The model family includes CatBoost, LightGBM, XGBoost and Random Forest. All models are used for training and K-fold cross-validation and early stopping are employed. The optimal model is selected based on the root mean square error (RMSE).

[0107] S8. Based on the optimal model in S7, the global and individual interpretations are performed using the Shapley and SHAP interpretation methods to identify key topographic parameters and their influence trends and sensitive ranges on the target mechanical performance vector.

[0108] The specific process of S8 is as follows:

[0109] S81. Perform SHAP global interpretation based on the optimal model, and use the Shapley sum interpretation method (SHAP) to calculate the vector of target mechanical properties for each topographic parameter. The absolute mean of Shapley's contribution values As a measure of the global importance of this morphological parameter, a SHAP global importance graph is generated, sorted from largest to smallest contribution, and the final set of key morphological parameters is determined based on the principle of relevance redundancy removal.

[0110] S82. Based on the median prediction samples, perform SHAP individual interpretation, select typical samples whose prediction results are near the median of the statistical distribution of the test set, and interpret them through SHAP force plots or by analyzing their key morphological parameters. , and The positive or negative contribution can be used to obtain a quantifiable mapping relationship;

[0111] S83. Combining the global and individual interpretation results of SHAP, the contribution direction, contribution magnitude and sensitive range of the morphological parameters in different value ranges are comprehensively determined to obtain the main trend of the key morphological parameters on the above mechanical properties and their variation range, and based on this, parameter action rules that can be used for engineering design are formed.

[0112] Specific Implementation Example 1: This embodiment mainly uses one-dimensional relative density scanning of the elastic modulus of the diamond-sheet; the same method can be extended to other TPMS or rod lattices such as G-surface and P-surface.

[0113] 1. Geometric acquisition;

[0114] like Figure 2 As shown, import or generate the target TPMS (Diamond-sheet) series model files and uniformly perform the following: centroid alignment and scale normalization to ensure that the spatial reference of each sample is consistent; mesh denoising and sharp angle blunting to avoid local curvature singularities or numerical instability; unit cell boundary and array periodization to ensure the geometric continuity of the periodic lattice under boundary conditions; volume fraction analysis and relative density derivation, calculating the relative density based on the ratio of the model entity volume to the envelope volume.

[0115] 2. Morphological characteristics;

[0116] Running the morphology parameter extraction script yields X: RD, Area, SSA, I1InertiaI1, I2InertiaI2, I3InertiaI3, H mean H std H med H iqr K mean K std K med K iqr CN mean CN std Degree Entropy;

[0117] 3. Mechanical measurements;

[0118] Obtain engineering force-displacement curves through uniaxial compression experiments or simulations;

[0119] Take the slope of the tangent line of the elastic segment; Press 0.2 Yield strength obtained by the offset method;

[0120] Defined as pre-peak strain Integrals:

[0121]

[0122] Sample pairs recording morphological parameter vectors and mechanical property vectors ,in .

[0123] 4. Density constraint;

[0124] Equal density or bandwidth constraints:

[0125] In the data modeling process, isodensity or bandwidth density constraints are applied to the samples. Isodensity constraint refers to fixing the relative density of the samples to a target value. The relative density of the bandwidth density constraint instruction samples lies within the interval Within the range, lower weights are assigned to samples at the interval boundaries to mitigate edge effects.

[0126] Relative density is used as an anchor feature throughout the entire quality control process. The cross-sectional comparison of samples and the generation of augmented data are all processed with relative density as a stratification or conditional variable, thereby avoiding performance confounding or statistical bias caused by density differences and ensuring fair evaluation and robust modeling between configurations under the condition of comparable density.

[0127] 5. Generate candidate enhancement strategies;

[0128] Strategy A: Jitter and Hybrid Enhancement Strategy (Freeze RD / Porosity / Rel_Density fields; key topography parameters can be scaled to adjust jitter amplitude).

[0129] Strategy B, a connection function enhancement strategy based on relative density conditionation (fitting Gaussian connection functions to continuous feature groups in hierarchical order according to relative density, and sampling discrete or narrow-domain features with self-sampling or low-noise sampling), is suitable for maintaining the joint distribution of relative density and morphology.

[0130] 6. Automatically switch to the optimal option based on consistency evaluation;

[0131] Marginal consistency: 0.05, 0.25;

[0132] Related structures: relative density-morphology parameter pairs 0.10;

[0133] The optimal strategy is selected from two categories: jitter and hybrid enhancement strategy and connection function enhancement strategy based on relative density conditionalization. The selection criterion is whether a threshold is met. , , .

[0134] When the threshold is detected , , If all requirements are met, continue executing the dithering and hybrid enhancement strategy; when a threshold is detected... , , If 1 to 3 of the requirements are not met, the gatekeeper is triggered to back off, and the connection function enhancement strategy based on relative density conditionalization is switched first and the layering and perturbation amplitude are refined.

[0135] like Figure 4 As shown, Figure 4 Part A is a comparison chart of the predicted value Pred and the true value True (Pred vs True), showing the model's fitting accuracy on the training set and the test set; Figure 4 Part B is the standardized residual distribution, which reflects the concentration and symmetry of model errors; Figure 4 Part C is the Predicted vs. Residuals graph, used to verify the randomness and uniformity of the residuals; Figure 4 Part D is the normal probability plot (QQ Plot), used to test the degree of agreement between the residual distribution and the theoretical normal distribution.

[0136] 7. The SHAP method model identifies key topographic parameters and their impact on the mechanical properties of the target.

[0137] like Figure 5-6 As shown, by using Shapley and the interpretation method SHAP to interpret the global and individual data, key topographic parameters and their influence trends and sensitive ranges on the target mechanical performance vector are identified.

[0138] Relative density RD and elastic modulus Yield strength and the energy absorbed The significant positive correlation indicates that as the volume fraction of the structural entity increases, the overall stiffness of the lattice and its energy absorption capacity increase simultaneously.

[0139] Specific surface area SSA and mean Gaussian curvature K mean (More negative) and standard deviation K std and The synergistic enhancement trend indicates that the increase in surface connectivity and pore complexity contributes to the improvement of energy absorption channel density.

[0140] When the standard deviation of the mean curvature H std Interquartile range H iqr When the value is too high, it can easily cause localized stress concentration and structural instability, affecting the yield strength. It exhibits a nonlinear effect.

[0141] I1InertiaI1, I2InertiaI2, and I3InertiaI3 reflect the geometrical anisotropy of inertia and elastic modulus. The growth of these parameters has a synergistic effect, indicating that the geometric distribution balance makes a significant contribution to the overall stiffness.

[0142] In summary, the results of this embodiment demonstrate the quantitative correspondence between structural geometry and macroscopic mechanical properties, and the feature thresholds and parameter ranges are automatically identified and output by the SHAP interpretable model. Specific Implementation Example 2:

[0144] When migrating the analysis process of Diamond-sheet (three-period minimum surface) lattice to bar lattice, only targeted adjustments are needed to the morphology parameter system and data consistency verification parameters; the other steps remain the same.

[0145] Specifically, the bar lattice uses a periodic network composed of bar segments and nodes as its basic unit, and its core morphological—topological characteristic parameters—include:

[0146] Number of support segments in the X, Y, and Z directions (X SC Y SC Z SC ) and the number of inclined support segments (Inclined) SC ), used to characterize the load-bearing channel density in the main axis and non-main axis directions;

[0147] Standard deviation of the distribution of the midpoint of the support along the three axes (MidX) Std MidY Std MidZ Std (This is used to measure the uniformity of the spatial distribution of the pole segments and the degree of local stress concentration;)

[0148] Mean and standard deviation of node connectivity (CN) mean CN std ) and the number of unit cell loops (Euler PC), used to characterize topological complexity and the diversity of load transfer paths;

[0149] Mean curvature and Gaussian curvature and their dispersion in the nodal region (Mean Cur MeanGau, Std Cur Std Gau (), used to describe the smoothness of node geometric transitions and potential instability susceptibility.

[0150] The above parameters constitute the main morphology-topology description system of the bar lattice, and participate as morphology parameter vectors in the training, prediction and interpretability analysis of subsequent machine learning models.

[0151] Therefore, the present invention adopts a metamaterial design method based on density constraints and interpretable AI, which not only ensures the comparability and interpretability of different types of lattices under equal density conditions, but also ensures the reliability of model predictions through consistency enhancement and verification closed loop, significantly reducing the cost of traditional experimental iteration and parameter trial and error. It provides a solution that can be directly implemented for lattice configuration design and performance prediction in the field of additive manufacturing, and has broad industrial application prospects.

[0152] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for metasurface design based on density constraints and explainable AI, characterized in that: Includes the following steps: S1. Obtain the geometric data of metamaterials to generate a 3D model; S2, running a topography parameter extraction script from the three-dimensional model generated in S1 to obtain a topography parameter vector ; The metamaterial includes a three-period minimal surface (TPMS) lattice and a truss lattice, and when the metamaterial is the TPMS lattice, a morphology parameter vector includes a total surface area Area, a specific surface area SSA, a first principal inertia I1, a second principal inertia I2, a third principal inertia I3, a mean curvature weighted mean H mean , a mean curvature standard deviation H std , a mean curvature median H med , a mean curvature interquartile range H iqr , a Gaussian curvature weighted mean K mean , a Gaussian curvature standard deviation K std , a Gaussian curvature median K med , a Gaussian curvature interquartile range K iqr , a mean connectivity CN mean , a connectivity standard deviation CN std , a degree distribution entropy DegreeEntropy; When the metamaterial is a truss lattice, including SSA, X-direction strut segment number X SC , Y-direction strut segment number Y SC , Z-direction strut segment number Z SC , Inclined strut segment number Inclined SC , Midpoint distribution standard deviation in X direction MidX Std , Midpoint distribution standard deviation in Y direction MidY Std , Midpoint distribution standard deviation in Z direction MidZ Std , Average connectivity CN mean , Connectivity standard deviation CN std , Average Euler number of unit cell Euler PC , Average Mean of node curvature Mean Cur , Standard deviation of node curvature Std Cur , Average Mean of node Gaussian curvature Mean Gau , Standard deviation of node Gaussian curvature Std Gau ; S3, performing mechanical measurement on the metamaterial of S1 to obtain a mechanical performance vector ; S4. Set density constraint conditions based on the metamaterial in S1; After S5 and S4 are completed, the shape parameter vector is... and mechanical property vector The training set is used to generate candidate augmentation strategies; S6. Based on the morphological parameter vector Calculate marginal consistency and relevant consistency indices and combine them with S5 to select the optimal enhancement strategy; After S7 and S6 are completed, the optimal model is obtained by selecting models based on the family of ensemble learning models. S8. Based on the optimal model in S7, the global and individual interpretations are performed using the Shapley and SHAP interpretation methods to identify key morphological parameters and their influence trends and sensitive ranges on the target mechanical performance vector.

2. The metamaterial design method based on density constraints and interpretable AI according to claim 1, characterized in that: S3 mechanical property vector ,in, Indicates the elastic modulus. For yield strength, This means by 0.2 Yield strength obtained by the offset method The specific energy absorption value is calculated using the formula for integrating the stress-strain curve over the strain interval before the peak. , Indicates engineering strain. This represents the maximum effective strain of a material before it reaches its peak stress.

3. The metamaterial design method based on density constraints and interpretable AI according to claim 1, characterized in that: The density constraints of S4 include isodense, bandwidth density, and relative density RD; To ensure that different metamaterial samples can be compared and analyzed and model trained under the same relative density (RD) conditions. To achieve isodensity constraints, where The target relative density constant is a pre-selected value used to represent the nominal relative density level of each metamaterial sample under isodense conditions. To impose restrictions on the density distribution, only data points or regions with density falling within a certain interval are considered. Implement bandwidth density constraints and perform weighted sampling, where This is the minimum relative density value accepted for bandwidth density comparison, corresponding to the lowest permissible relative density for TPMS and rod-lattice metamaterials under requirements of manufacturing precision, minimum geometric wall thickness, and mechanical stability. The maximum relative density value accepted for bandwidth density comparison corresponds to the highest relative density allowed under equivalent volume conditions for metamaterials of the TPMS lattice and rod lattice types. The relative density RD is a fixed value, that is Or located in the interval Internally, relative density RD is used as the anchor parameter to perform screening, normalization and weighting processing on the sample data to ensure the comparability and consistency of different metamaterials or batches of samples on the density scale.

4. The metamaterial design method based on density constraints and interpretable AI according to claim 3, characterized in that: The quality control measures for relative density RD as an anchor point parameter are as follows: Based on the criterion of high correlation with relative density RD and non-excessive collinearity, a pairing set of relative density RD and morphological parameters is selected. The redundancy removal criterion between morphological parameters is set as follows: 0.98, of which, Represents any two topographic parameters and The Pearson correlation coefficient between them 0.98 indicates that the absolute value of the correlation coefficient between the two morphological parameters does not exceed 0.98; For each pair of relative density-morphology parameters, the Pearson correlation coefficient was calculated. and ,in, This represents the Pearson correlation coefficient between the relative density RD in the original training dataset and the morphological parameter under the current RD stratification conditions. This represents the Pearson correlation coefficient of the corresponding RD-morphology parameter pairs in the augmented dataset. For statistical equivalence testing, the above correlation coefficient is... The transformation maps to an approximately normal distribution space and is used to measure the statistical bias of the structural differences between the augmented and original data; the difference is... Defined as: ； in, The inverse hyperbolic tangent function is used to map the Pearson correlation coefficient to... The space is made to approximately follow a standard normal distribution in order to perform statistical equivalence tests, when The 95% confidence upper bound is satisfied. At that time, among them For tolerance zone and If so, it is determined that the correlation structure between the augmented data and the original data at the relative density anchor point is statistically equivalent; If it exceeds the tolerance zone If this occurs, it indicates that the enhancement process has disrupted the natural correlation structure between the relative density and morphology parameter pairings. The enhancement strategy should be adjusted or the perturbation amplitude reduced until the data distribution consistency is restored.

5. The metamaterial design method based on density constraints and interpretable AI according to claim 4, characterized in that: S5's candidate enhancement strategies include a dithering and hybrid enhancement strategy and a connection function enhancement strategy based on relative density conditionalization. The details of these two strategies are as follows: The jitter and blending enhancement strategy, targeting continuous topographic parameters and mechanical performance indicators, performs the following random perturbation and sample blending operations on the topographic parameter vector. and mechanical property vector Gaussian perturbations were applied respectively to obtain and As shown below: ； ； in, for Samples after applying Gaussian perturbation The symbol for element-wise multiplication. Original sample The amplitude of the disturbance and , Mechanical property vector Samples after applying Gaussian perturbation It follows a normal distribution. Let represent the random perturbation factor applied to the topographic parameter vector , which follows a zero-mean normal distribution. To represent the vector of mechanical properties applied The random disturbance factor follows a zero-mean normal distribution. Original sample The amplitude of the disturbance and The relative density RD remains frozen during this stage to ensure that the enhanced samples are within the same density anchor layer; Select any two pairs of samples after applying Gaussian perturbation , The two mixed samples are obtained by performing linear mixing based on the beta distribution. , The details are as follows: ； ； in, for and The mixed sample, for and Mixed samples, mixing coefficient The random mixing coefficients are in the interval 0 to 1, used to linearly weight the morphological parameter vectors and mechanical performance indices of any two sets of samples. Obtain the parameter as of Distribution, its probability density function for: ,in, for function; To control the distribution shape parameter of the mixing degree, when When the value is in the range of 0.2 to 0.6, the generated The values ​​tend to be closer to 0 or 1, making the mixed samples closer to one of the original samples, thereby enhancing the differences between samples and avoiding over-smoothing; Based on a relative density-conditionalized connectivity function enhancement strategy, under equal density or bandwidth density constraints, connectivity function enhancement is performed on continuous features using 4–6 binning layers based on quantiles as conditional variables, with each topographic parameter vector as the conditional variable. The process of performing normal join function mapping is as follows: ； in, It is the standard normal distribution function. It is the inverse function of the standard normal distribution. It is the empirical distribution function; The correlation matrix of Gaussian connection functions between fitted features within each density sublayer is calculated. And perform multivariate normal sampling to generate new enhanced morphology parameter samples. and Then, an inverse transformation is performed to obtain the reconstructed topographic parameter vector. and For discrete parameters or parameters with narrow numerical ranges, bootstrap sampling or adding small perturbations can be used to enhance the samples. The settings for adding small perturbations are as follows: and The perturbation amplitude is used to introduce finite randomness to prevent complete duplication of augmented samples while ensuring the physical feasibility of the parameters.

6. The metamaterial design method based on density constraints and interpretable AI according to claim 5, characterized in that: In S6, the marginal consistency index and the relevant consistency index are the judgment thresholds for selecting the optimal enhancement strategy. The marginal consistency index is... , ,in Tested for Kolmogorov–Smirnov The value is used to measure whether the marginal distributions of augmented data and original data on the same morphological parameter are statistically consistent; The normalized result of the first Wasserstein distance is used to measure the degree of distributional offset between the augmented data and the original data on the same topographic parameter, and is a relevant consistency index. The absolute difference between the Pearson correlation coefficients of relative density RD and morphology parameters before and after data augmentation is given. The threshold requirements for all indicators are as follows: Must meet , Must meet , Must meet .

7. The metamaterial design method based on density constraints and interpretable AI according to claim 6, characterized in that: The process of selecting the optimal enhancement strategy in S6 is as follows: The optimal strategy is selected from two categories: jitter and hybrid enhancement strategies, and connection function enhancement strategies based on relative density conditionalization. The selection criterion is whether a threshold is met. , , ; When the threshold is detected , , If all requirements are met, continue executing the dithering and hybrid enhancement strategy; when a threshold is detected... , , If 1 to 3 of the requirements are not met, the gatekeeper is triggered to back off, and the connection function enhancement strategy based on relative density conditionalization is switched first and the layering and perturbation amplitude are refined.

8. The metamaterial design method based on density constraints and interpretable AI according to claim 7, characterized in that: The S7 model family includes CatBoost, LightGBM, XGBoost, and Random Forest. All models are used for training, and K-fold cross-validation and early stopping are employed. The optimal model is selected based on the root mean square error (RMSE).

9. The metamaterial design method based on density constraints and interpretable AI according to claim 8, characterized in that: The specific process of S8 is as follows: S81. Perform SHAP global interpretation based on the optimal model, and use the Shapley sum interpretation method (SHAP) to calculate the vector of target mechanical properties for each topographic parameter. The absolute mean of Shapley's contribution values As a measure of the global importance of this morphological parameter, a SHAP global importance graph is generated, sorted from largest to smallest contribution, and the final set of key morphological parameters is determined based on the principle of relevance redundancy removal. S82. Based on the median prediction samples, perform SHAP individual interpretation, select typical samples whose prediction results are near the median of the statistical distribution of the test set, and interpret them through SHAP force plots or by analyzing their key morphological parameters. , and The positive or negative contribution can be used to obtain a quantifiable mapping relationship; S83. Combining the global and individual interpretation results of SHAP, the contribution direction, contribution magnitude and sensitive range of the morphological parameters in different value ranges are comprehensively determined to obtain the main trend of the key morphological parameters on the above mechanical properties and their variation range, and based on this, parameter action rules that can be used for engineering design are formed.

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