A method for constructing a three-dimensional local entropy gradient feature of a porous structure for machine learning modeling

Abstract

The application discloses a kind of porous structure three-dimensional local entropy gradient feature construction methods for machine learning modeling, the method is first to the voxelization processing of three-dimensional model, constructs three-dimensional binary voxel matrix, subsequently based on sliding window, obtain local probability distribution, and utilize information entropy principle to construct three-dimensional local entropy field, on this basis, by space gradient operation obtains entropy gradient vector field and its modulus distribution, further according to entropy gradient size extraction structure change violent area, realize the identification of porous structure key feature area, finally constructs multidimensional feature vector, as the feature description of porous structure, for structure optimization analysis or performance prediction.The method of the application can effectively represent the spatial complexity and local non-uniformity of porous structure, has the advantages of strong feature expression ability, clear data structure, easy to couple with machine learning algorithm, etc., can be widely applied in additive manufacturing structure design optimization, porous material mechanics performance prediction and intelligent manufacturing field.

Description

Technical Field

[0001] This invention belongs to the field of additive manufacturing and porous material structure analysis technology, specifically relating to a method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling. Background Technology

[0002] With the rapid development of metal additive manufacturing technology, porous structures (such as lattice structures, TPMS structures, and biomimetic porous structures) have been widely used in aerospace, biomedical, and high-end equipment fields due to their excellent mechanical properties, energy absorption characteristics, and lightweight advantages. These structures possess complex three-dimensional spatial distribution characteristics; their geometric non-uniformity, local complexity, and spatial variation gradient directly determine the forming quality, mechanical response, and failure behavior of the components. Therefore, accurate, quantitative, and multi-scale characterization of porous structures is a crucial prerequisite for structural optimization design, process control, and performance prediction.

[0003] Existing methods for characterizing porous structures mainly rely on macroscopic geometric or topological parameters, such as porosity, pore size, specific surface area, connectivity, and number of nodes. While these parameters can reflect the macroscopic characteristics of the structure to some extent, their characterization dimensions are limited and their physical meaning is insufficient to meet the needs of high-precision design and intelligent modeling. The currently published related patents still have significant technical defects: For example, the invention patent with publication number CN110702580A discloses "A method for characterizing the heterogeneity of pore throats in tight sandstone reservoirs based on information entropy". This method only calculates the global information entropy based on the pore throat radius distribution, which can only achieve overall uniformity evaluation, but cannot achieve three-dimensional local structure analysis, let alone involve the calculation of local entropy gradient; the invention patent with publication number CN113792482A discloses "A method for characterizing and analyzing the three-dimensional structure of porous media", which only uses traditional geometric parameters for description, does not introduce information entropy-related theories, and cannot quantitatively characterize the complexity of local structures; the invention patent with publication number CN115830226A discloses "A method for three-dimensional reconstruction of porous media", which only achieves structural visualization and macroscopic performance prediction, but does not have the ability to identify areas with drastic structural changes, nor can it extract high-dimensional feature vectors that can be used for machine learning.

[0004] In summary, existing technologies generally suffer from the following shortcomings: 1. They can only describe the structure at the macroscopic level and cannot reflect the non-uniform distribution characteristics of porous structures in three-dimensional space; 2. They are mainly based on global statistics and are difficult to quantitatively characterize the structural complexity of local regions; 3. They lack the ability to accurately identify and locate regions with abrupt structural changes and drastic gradient changes; 4. The characterization parameters are of a single dimension and have weak correlation, making them difficult to use as efficient features directly for the construction of machine learning models.

[0005] In recent years, information entropy has been used to describe the complexity and disorder of a system. However, existing research and patents are mostly focused on two-dimensional image analysis or overall entropy statistics. There are no methods for calculating the local entropy of three-dimensional porous structures and representing their spatial gradients. Therefore, it is impossible to simultaneously describe the local complexity of the structure and quantify the spatial variation law.

[0006] Therefore, the industry urgently needs a porous structure characterization method that can take into account three-dimensional local features, spatial gradient changes, and can be used for intelligent modeling to make up for the shortcomings of existing technologies. Summary of the Invention

[0007] The technical problem this invention aims to solve is to address the shortcomings of the prior art by providing a method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling. This method constructs a local entropy field and its gradient field to accurately characterize the complexity and spatial variation characteristics of porous structures, and uses this information for identifying key structural regions and performing performance analysis. This solves the problem that existing methods are unable to quantitatively characterize the spatial complexity and local non-uniform variation characteristics of porous structures, and are difficult to directly apply to machine learning modeling.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling, characterized in that the method includes the following steps: Step 1: 3D structure voxelization: A three-dimensional model of the porous structure is obtained, and the three-dimensional model is voxelized to obtain a three-dimensional binary voxel matrix. The voxel value is either solid or pore, with solid parts assigned a value of 1 and pore parts assigned a value of 0. Step 2: Local probability calculation: A three-dimensional sliding window is constructed in the three-dimensional binary voxel matrix obtained in step one. Each local region is divided, and the probability distribution of solid voxels and pore voxels in each local region is statistically analyzed. Step 3: Calculate the entropy value of each local region: Based on the probability distribution obtained in step two, and using the information entropy formula, the entropy value of each local region is calculated: ;in, For entity voxel probability, The probability of a pore voxel; Step 4: Construct a three-dimensional local entropy field: A three-dimensional local entropy field is constructed based on the entropy values ​​of each local region calculated in step three. ; Step 5: Spatial gradient calculation: The three-dimensional local entropy field constructed in step four Perform spatial gradient calculation to obtain the three-dimensional local entropy gradient vector: The three-dimensional local entropy gradient vectors at all spatial locations together constitute the entropy gradient vector field. Further calculations are performed on the magnitude of the three-dimensional local entropy gradient. The magnitudes of the three-dimensional local entropy gradients at all spatial locations collectively constitute the entropy gradient magnitude field; among them, , and Let X, Y, and Z represent the gradient components of the local entropy field in the X, Y, and Z directions, respectively. This represents the overall intensity of local entropy changes; Step 6: Extraction of high gradient regions: Based on the spatial distribution characteristics of the three-dimensional entropy gradient magnitude field constructed in step five, high-gradient regions are extracted from the drastically changing areas in the structure. A statistical quantile method is used to set a high-gradient threshold, where the voxel position satisfies the following conditions: At that time, the voxel was identified as a high gradient region, in which The volume fraction of the high gradient region is calculated under the given threshold. Step 7: Feature Construction and Application The three-dimensional local entropy field constructed in step four, the entropy gradient vector field and entropy gradient magnitude field constructed in step five, and the volume fraction of the high gradient region obtained in step six are used to construct a multi-dimensional feature vector as a feature description of the porous structure, which is used for structural optimization analysis or performance prediction.

[0009] This invention first performs voxelization (discretization) on the three-dimensional model of the porous structure to construct a three-dimensional binary voxel matrix. Then, based on a three-dimensional sliding window, each local region is divided, and the volume fraction of the solids in the neighborhood of each local region, i.e., each voxel point, is calculated to obtain the probability distribution of the solid voxels. ,in, The number of entity voxels within the 3D sliding window. Given the total number of voxels in the 3D sliding window, a 3D local entropy field is constructed based on the local probability distribution and the principle of information entropy. Specifically, the local entropy value at each voxel location is calculated using the information entropy formula. ,in, That is, the probability distribution of entity voxels , That is, the probability distribution of pore voxels Based on the calculated entropy values ​​of each local region, a three-dimensional local entropy field is obtained. Furthermore, the three-dimensional local entropy gradient vector is obtained through spatial gradient calculation. The gradient vectors at all spatial locations together constitute the entropy gradient vector field. Furthermore, the magnitude of the three-dimensional local entropy gradient vector is calculated to obtain the magnitude of the three-dimensional local entropy gradient. The three-dimensional local entropy gradient magnitudes at all spatial locations together constitute the entropy gradient magnitude field. Based on the three-dimensional entropy gradient magnitude field, regions with drastic structural changes are further extracted according to the magnitude of the entropy gradient. A threshold is set, preferably a statistical quantile threshold, to extract high gradient regions for identifying regions with drastic structural changes, thereby realizing the identification of key feature regions of porous structures. The volume fraction of high gradient regions is calculated, and finally, a multi-dimensional feature vector is constructed to realize the performance prediction and structural optimization analysis of porous structures.

[0010] This invention specifically relates to a method for constructing information entropy features based on three-dimensional voxel data, and more particularly to a method for quantitatively characterizing the spatial complexity and local variation features of porous structures by constructing a three-dimensional local entropy field and its gradient field. This method can extract and construct multi-dimensional feature vectors suitable for machine learning modeling, and can be used for performance prediction and structural optimization analysis of porous structures.

[0011] The aforementioned method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling is characterized in that the porous structure in step one includes solid rod structures, hollow rod structures, and regular or irregular lattice structures. The method of this invention is applicable to various types of porous structures; furthermore, it is also applicable to continuous porous structures and biomimetic structures, exhibiting good structural adaptability and versatility.

[0012] The aforementioned method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling is characterized in that the voxel size in step one is set according to the feature size of the porous structure, specifically 1 / 5 to 1 / 10 of the structural feature size. This structural feature size is the smallest feature scale in the porous structure, including the diameter of the rods, the pore size, or the smallest unit cell size. In this invention, the voxel size of the voxel processing is adaptively set according to the feature size of the porous structure to achieve a balance between structural detail representation and computational efficiency. The preferred structural feature size is the diameter of the rods. Through this setting, the computational complexity can be effectively reduced while ensuring accurate representation of the porous structure's geometry, thereby improving the method's engineering applicability.

[0013] The aforementioned method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling is characterized in that the three-dimensional sliding window in step two is a cubic window with a size of n×n×n, where n is an integer greater than or equal to 3. In this invention, the window size n is selected as 3, 5, or 7 to adapt to the feature analysis needs of structures at different scales. By traversing the voxel matrix point by point through this three-dimensional sliding window, entity distribution information within a local spatial range can be obtained, thereby achieving multi-scale representation of the local features of the structure.

[0014] The aforementioned method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling is characterized in that the three-dimensional local entropy field in step four is constructed by mapping the entropy value corresponding to the center position of a three-dimensional sliding window to a three-dimensional space. In this invention, for each voxel point, the local entropy value calculated within its neighborhood window is assigned to that voxel position, thereby forming a three-dimensional entropy field that corresponds one-to-one with the original structural space, realizing the continuous expression of structural complexity in space.

[0015] The aforementioned method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling is characterized in that the spatial gradient calculation in step five is performed using a finite difference method, including central difference or forward difference. This invention employs the central difference method to improve the numerical accuracy of gradient calculation. This method calculates the gradient components of the entropy field in the X, Y, and Z directions respectively, thereby constructing a complete entropy gradient vector field.

[0016] The aforementioned method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling is characterized in that the three-dimensional local entropy values ​​and their gradient-related component values ​​in step five include the average entropy value, entropy standard deviation, average gradient in the X direction, average gradient in the Y direction, average gradient in the Z direction, and maximum gradient value. Through the above statistical processing, this invention achieves a quantitative description of the degree of local change in the structure and its spatial distribution pattern.

[0017] The aforementioned method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling is characterized by fusing geometric parameter features with the multi-dimensional feature vector constructed in step six; the geometric parameter features include relative density, porosity, specific surface area, and rod dimensions. This invention significantly enhances the comprehensive characterization ability of porous structures by fusing entropy features with geometric features, providing a more comprehensive information foundation for subsequent performance prediction.

[0018] The aforementioned method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling is characterized in that the multidimensional feature vectors are used for training the machine learning model to predict the mechanical properties of the porous structure. The machine learning model in this invention includes support vector machines, random forests, XGBoost, and neural networks, etc., which establish a mapping relationship between structural features and mechanical properties to achieve efficient prediction of performance parameters such as elastic modulus, strength, and energy absorption.

[0019] The aforementioned method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling is characterized by its ability to identify local non-uniform regions or potential failure regions in porous structures. In this invention, by analyzing regions with high entropy gradient values, the method can identify locations of geometrical abrupt changes and areas where stress concentration may occur in the structure, thus providing important basis for structural optimization design and engineering applications.

[0020] This invention further improves the accuracy and applicability of porous structure characterization, and enhances the practicality and reliability of the method in engineering applications.

[0021] Compared with the prior art, the present invention has the following advantages: 1. Capable of quantitatively characterizing the complexity of three-dimensional structures: This invention performs three-dimensional voxelization on porous structures and constructs a local probability distribution based on a three-dimensional sliding window. Furthermore, it utilizes information entropy theory to establish a three-dimensional local entropy field, thereby achieving a quantitative description of the spatial distribution characteristics of the structure. Compared with traditional characterization methods based on single geometric parameters such as porosity and pore size, this invention can characterize the uncertainty and complexity of the structure in space from an information theory perspective. It can reflect the uniformity and randomness of the distribution of entities and pores inside the porous structure, thus improving the accuracy of structural description.

[0022] 2. Capable of accurately identifying structural abrupt changes and sensitive regions: This invention calculates the spatial gradient of a three-dimensional local entropy field to obtain the entropy gradient vector field and its magnitude distribution. Based on the gradient threshold, high gradient regions are extracted. These regions correspond to locations where the distribution of solids and pores in a structure changes rapidly, such as pore wall boundaries, connecting nodes, and geometric transition regions. Compared with traditional methods that struggle to identify local structural changes, this invention can accurately locate regions of structural abrupt changes. It can be used to identify potential stress concentration areas, failure initiation areas, and structurally weak areas, and has significant engineering implications.

[0023] 3. It has stronger characterization capabilities and can reflect structural non-homogeneity and anisotropy: Traditional structural characterization methods often rely on overall statistical parameters, which are difficult to reflect local differences. This invention constructs a three-dimensional local entropy field and its gradient field, which can not only describe the overall complexity of the structure, but also reveal the variation characteristics of the structure in different spatial locations. At the same time, by analyzing the components of the entropy gradient in the X, Y, and Z directions, the anisotropic characteristics of the structure can be further characterized, thereby achieving a fine characterization of complex lattice structures and non-uniform structures, and significantly improving the characterization capability.

[0024] 4. Can be used as a highly efficient feature for machine learning modeling: The entropy and entropy gradient features constructed in this invention have clear physical meaning and good numerical stability. They can be transformed into multidimensional feature vectors (including average entropy, entropy variance, gradient mean, maximum gradient value, and the proportion of high gradient regions). Compared with traditional geometric features, these features can more comprehensively reflect the spatial information of the structure, which helps to improve the training efficiency and prediction accuracy of machine learning models (such as support vector machines, random forests, XGBoost, and neural networks). They are suitable for predicting the mechanical properties of porous structures and optimizing structural design.

[0025] 5. The method is highly versatile and has a wide range of applications: This invention is based on voxel data and information entropy theory. It does not depend on specific structural forms or material types and has good versatility. The method is applicable to a variety of typical porous structures, including but not limited to: lattice structures, TPMS structures, biomimetic porous structures, and additive manufacturing complex porous structures. At the same time, the method is compatible with 3D model data from different sources, such as STL and CT reconstruction data, and has good engineering adaptability and promotion value.

[0026] 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

[0027] Figure 1 This is a flowchart illustrating the method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling, as described in this invention.

[0028] Figure 2 This is a model diagram of a complex porous lattice structure with a rectangular three-dimensional gradient frame in Embodiment 1 of the present invention.

[0029] Figure 3 This is a voxelized result of the complex porous lattice structure model of the rectangular three-dimensional gradient frame in Embodiment 1 of the present invention.

[0030] Figure 4 This is a three-dimensional local probability field distribution diagram of the complex porous lattice structure of the rectangular three-dimensional gradient frame in Embodiment 1 of the present invention.

[0031] Figure 5 This is a three-dimensional local information entropy field distribution diagram of the complex porous lattice structure of the rectangular three-dimensional gradient frame in Embodiment 1 of the present invention.

[0032] Figure 6 This is a three-dimensional entropy gradient distribution diagram of the complex porous lattice structure of the rectangular three-dimensional gradient frame in Embodiment 1 of the present invention.

[0033] Figure 7 This is a three-dimensional entropy gradient magnitude distribution diagram of the complex porous lattice structure of the rectangular three-dimensional gradient frame in Embodiment 1 of the present invention.

[0034] Figure 8 This is a three-dimensional high gradient region entropy field distribution diagram of the complex porous lattice structure of the rectangular three-dimensional gradient frame in Embodiment 1 of the present invention.

[0035] Figure 9 This is a model diagram of a complex porous lattice structure with extremely small curved surfaces in Embodiment 2 of the present invention.

[0036] Figure 10 This is a graph showing the results of the solidification of the complex porous lattice structure with extremely small curved surfaces in Embodiment 2 of the present invention.

[0037] Figure 11 This is a three-dimensional local probability field distribution diagram of the complex porous lattice structure with minimal curved surfaces in Embodiment 2 of the present invention.

[0038] Figure 12 This is a three-dimensional local information entropy field distribution diagram of the complex porous lattice structure with minimal curved surfaces in Embodiment 2 of the present invention.

[0039] Figure 13 This is a three-dimensional entropy gradient distribution diagram of the complex porous lattice structure with minimal curved surfaces in Embodiment 2 of the present invention.

[0040] Figure 14 This is a three-dimensional gradient modulus distribution diagram of the complex porous lattice structure with minimal curved surface in Embodiment 2 of the present invention.

[0041] Figure 15 This is the entropy distribution diagram of the three-dimensional high gradient region of the complex porous lattice structure with minimal curved surface in Embodiment 2 of the present invention. Detailed Implementation

[0042] Figure 1 This is a flowchart illustrating the method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling, as described in this invention. Figure 1 As can be seen from the above, the present invention includes the following steps: Step 1, three-dimensional structure voxelization; Step 2, local probability calculation; Step 3, calculation of entropy values ​​of each local region; Step 4, construction of a three-dimensional local entropy field; Step 5, spatial gradient calculation; Step 6, extraction of high gradient regions; and Step 7, feature construction and application for structural optimization analysis or performance prediction.

[0043] Example 1 This embodiment includes the following steps: Step 1: 3D structure voxelization: A complex porous lattice structure with a rectangular gradient frame measuring 8mm × 10mm × 10mm was generated using the additive manufacturing software Magics 3D modeling software. (See...) Figure 2 The model was named Box_Rescaled(0.800-1.000-1.000) and saved as an STL file. The Jupyter Notebook program editor was used to read the 3D model "Box_Rescaled(0.800-1.000-1.000).stl", and it was subjected to regular voxelization. The voxel resolution was set to 0.1 mm, with solid parts assigned a value of 1 and porous parts assigned a value of 0, resulting in a 3D binary voxel matrix. The total number of prime numbers obtained statistically is: The number of entity primes is: The porosity is: Then, substituting into the calculation formula: Entity voxel probability Empty voxel probability ,get: Substitute into the overall relative density calculation formula: To obtain the actual relative density: The output model after voxelization calculation is shown below. Figure 3 ; Step 2: Local probability calculation: A three-dimensional sliding window is constructed in the three-dimensional binary voxel matrix obtained in step one. Each local region is divided, and the ratio of the number of entity voxels in the neighborhood to the total number of voxels is calculated for each voxel point to obtain the local probability distribution. The calculation formula is as follows: ,in, The number of entity voxels within the 3D sliding window. Given the total number of elements in the 3D sliding window, the local probability distribution is mapped back to 3D space, and thresholding is performed only on the entity region to construct a 3D local probability field distribution map, see [link to map]. Figure 4 This figure is used to characterize the proportion of local entities near different locations in a porous lattice structure. The color bars in the figure change from blue to red, corresponding to local probabilities. The results show that the local probability value is higher in the main body region of the rod, indicating that the solid distribution in its neighborhood is relatively concentrated. However, the local probability value is relatively lower at the rod boundary, connection area, and corner transition position, indicating that solids and pores coexist in the neighborhood of these areas, which belong to the structural transition region. Therefore, the three-dimensional local probability field can not only reflect the local solid distribution characteristics of porous lattice structure, but also provide basic data support for the subsequent construction of three-dimensional local entropy field and entropy gradient field. Step 3: Calculate the entropy value of each local region: Based on the probability distribution obtained in step two, and using the information entropy formula, the entropy value of each local region is calculated: ,in, For entity voxel probability, The probability of a pore voxel; Step 4: Construct a three-dimensional local entropy field: A three-dimensional local entropy field is constructed based on the entropy values ​​of each local region calculated in step three. That is, based on the information entropy formula, the local entropy value of each voxel position is calculated. By mapping the entropy value to three-dimensional space, a local complexity distribution map of the porous lattice structure can be obtained, which is used to characterize the degree of mixing between solids and pores in local regions. See Figure 5The blue area has low local entropy, indicating that the area is almost entirely composed of solids or pores, with a relatively simple structure. The red area has high local entropy, indicating that the area is significantly mixed with solids and pores, with a high structural complexity. The boundary and transition regions usually have high entropy values ​​and are the key areas for subsequent entropy gradient analysis. Step 5: Spatial gradient calculation: The three-dimensional local entropy field constructed in step four with size (81, 101, 101) Perform spatial gradient calculation to obtain the three-dimensional local entropy gradient vector: The three-dimensional local entropy gradient vectors at all spatial locations together constitute the entropy gradient vector field, see... Figure 6 Further calculate the magnitude of the three-dimensional local entropy gradient: The three-dimensional local entropy gradient magnitudes at all spatial locations collectively constitute the entropy gradient magnitude field. Results show that the gradient components in the X, Y, and Z directions all range from -0.4854753 to 0.4854753, with a minimum magnitude of 0.0, a maximum of 0.5138984, and an average of 0.06400373. Furthermore, statistical analysis of the gradients in each direction within the solid region yields the three-dimensional average entropy gradient vectors as follows: , , The above results indicate that the local complexity of the porous lattice structure changes most significantly in the Y direction, while the change in the Z direction is relatively small, suggesting that the porous lattice structure has certain directional characteristics. Further mapping of the entropy gradient magnitude to the solid region for three-dimensional visualization yields a three-dimensional entropy gradient magnitude distribution map, see [see...]. Figure 7 This image can visually show the locations where the complexity of the structure changes dramatically, providing a basis for subsequent extraction of high gradient regions and identification of structurally sensitive areas; Step 6: Extraction of high gradient regions: Based on the spatial distribution characteristics of the three-dimensional entropy gradient magnitude field constructed in step five, high-gradient regions are extracted from the drastically changing areas in the porous lattice structure. Specifically, a statistical quantile method is used to set a high-gradient threshold, with the 90th quantile of the entropy gradient magnitude within the solid region as the criterion. When the voxel position satisfies: At that time, the voxel was identified as a high gradient region, in which The threshold value is set; through statistical analysis of the entropy gradient magnitude within the entity region, the threshold value is determined as follows: Under this threshold condition, the number of voxels extracted from the high gradient region is 14202, and the total number of entity voxels is 140181. Further calculation yields the volume fraction of the high gradient region as follows: The results show that high-gradient regions account for approximately 10.13% of the solid structure, indicating that only a small portion of the porous lattice structure exhibits significant complexity variations. This can be seen through 3D visualization. Figure 8 High gradient regions are mainly concentrated at member connection nodes, boundary corners, and locations of abrupt changes in structural geometry. These regions correspond to the locations where the distribution of solids and pores in porous lattice structures changes most drastically, and are usually potential stress concentration areas or failure-sensitive areas. Therefore, the extracted high gradient regions can effectively characterize the key geometric feature areas in porous lattice structures, providing an important basis for the performance analysis and optimization design of porous lattice structures. Step 7: Feature Construction and Application After constructing the three-dimensional local entropy field and entropy gradient field and extracting high-gradient regions in the aforementioned steps, the porous lattice structure is further feature-constructed to form a multi-dimensional feature vector that can be used for engineering analysis and machine learning modeling. Statistical analysis is performed on the three-dimensional local entropy field within the solid region to calculate the average entropy value and entropy standard deviation. The average entropy value characterizes the overall spatial complexity of the porous lattice structure, and the entropy standard deviation reflects the dispersion of the complexity distribution of the porous lattice structure. The calculated average entropy value is: The standard deviation of entropy is: Furthermore, the components of the entropy gradient vector field and the entropy gradient magnitude field in each spatial direction are statistically analyzed to calculate the average gradient value in each direction. This average gradient value is used to characterize the directional features of the complexity variation of the porous lattice structure, resulting in: , , The results show that the complexity of the porous lattice structure changes most significantly in the Y direction, exhibiting a clear directional characteristic. Furthermore, statistical analysis of the entropy gradient magnitude reveals that the maximum gradient value is: This value corresponds to the location in the structure where the local complexity changes most drastically, typically located in structural connection regions or regions of geometric abrupt changes. Furthermore, based on the high-gradient regions extracted in step six, their volume fraction within the solid region is calculated. The volume fraction of the high-gradient regions is: This indicates that approximately 10.13% of the region in the porous lattice structure belongs to the region of significant complexity variation; in summary, the constructed multidimensional feature vector is: The feature vectors correspond to the average entropy value, entropy standard deviation, average gradient in the X direction, average gradient in the Y direction, average gradient in the Z direction, maximum gradient value, and volume fraction of high gradient region, respectively. These feature vectors can comprehensively characterize porous lattice structures from multiple perspectives, such as overall complexity, spatial non-uniformity, directional variation, and degree of local mutation. They can be used as input for machine learning models for engineering applications such as predicting the mechanical properties of porous lattice structures, structural optimization design, and identification of failure-sensitive regions.

[0044] In this embodiment, the voxel size of the voxelization process is adaptively set according to the feature size of the porous structure to achieve a balance between structural detail representation and computational efficiency. The minimum feature size of the structure is the diameter of the rod, which is about 0.5 mm. The voxel size is selected as 0.1 mm, which is about 1 / 5 of the feature size. Through this setting, while ensuring the effective representation of the geometric boundary and connection features of the structure, the size of the voxel matrix is ​​controlled within (81, 101, 101), which effectively reduces the computational complexity and improves the computational efficiency and engineering applicability.

[0045] In this embodiment, the voxel size can also be selected as 0.05 mm, which is about 1 / 10 of the feature size, or the voxel size can be selected as 0.07 mm, which is about 1 / 7 of the feature size.

[0046] In this embodiment, the three-dimensional sliding window adopts the form of a cube window with a size of 5×5×5 for local probability statistics. By using a sliding window of this size, the local structural features can be fully expressed while avoiding the noise sensitivity problem caused by an excessively small window, thereby achieving stable extraction of local structural features.

[0047] In this embodiment, the three-dimensional sliding window adopts the form of a cube window, and its size can also be 3×3×3 or 7×7×7.

[0048] In this embodiment, the three-dimensional local entropy field is constructed by mapping the entropy value corresponding to the center position of the three-dimensional sliding window to the three-dimensional space. The entropy field is calculated through the local probability distribution, and its value ranges from 0 to 0.99995387, with an average entropy value of 0.12515032. The results show that this method can effectively distinguish between pure solid regions, pure porous regions, and transition regions, and realize the spatial continuous expression of structural complexity.

[0049] In this embodiment, the spatial gradient is calculated using the finite difference method, with the central difference method employed to improve calculation accuracy. By calculating the gradient of the entropy field, the gradient components in each direction range from -0.4854753 to 0.4854753, with a maximum gradient magnitude of 0.5138984 and an average value of 0.06400373, which can effectively reflect the spatial distribution characteristics of structural complexity changes.

[0050] In this embodiment, the spatial gradient is calculated using the finite difference method, and the forward difference method can also be used to improve the calculation accuracy.

[0051] In this embodiment, the multidimensional structural feature vector can be used as input data for machine learning model training to achieve performance prediction of porous structures. The models include support vector machines, random forests, XGBoost, and neural networks. By establishing a mapping relationship between structural features and mechanical properties, efficient prediction of properties such as elastic modulus, strength, and energy absorption can be achieved.

[0052] In this embodiment, the method can also be used to identify local non-uniform regions or potential failure regions in porous structures. High gradient regions are mainly distributed at structural connection nodes and geometric abrupt change locations. These regions usually correspond to potential stress concentration regions. By analyzing regions with high entropy gradient values, important basis can be provided for structural optimization design and engineering applications.

[0053] In this embodiment, the method is applicable to various types of porous structures, including solid rod lattice structures, hollow rod lattice structures, and regular or irregular lattice structures. At the same time, the method is also applicable to continuous porous structures and biomimetic porous structures, and has good versatility and adaptability.

[0054] Through the above embodiments, the present invention realizes the transformation of the complexity of porous structures from geometric description to information content description, which significantly improves the accuracy and stability of structural characterization, while taking into account computational efficiency and enhancing the practicality and reliability of the method in engineering applications.

[0055] Example 2 This embodiment includes the following steps: Step 1: 3D structure voxelization: A complex porous lattice structure with an extremely small curved surface (length × width × height) of 10mm × 10mm × 10mm was generated using the additive manufacturing software Magics 3D modeling software. (See...) Figure 9 Name it gyroid (10×10×10) and save it as an STL file. Use the Jupyter Notebook program editor to read the 3D model "gyroid(10×10×10).stl", perform regular voxelization on it, set the voxel resolution size to 0.1mm, assign a value of 1 to solid parts and a value of 0 to pore parts, and obtain a 3D binary voxel matrix: The total number of prime numbers obtained statistically is: The number of entity primes is: =302,840, the porosity is: =727,461, then substituting into the calculation formula: Entity voxel probability Empty voxel probability ,get: Substitute into the overall relative density calculation formula: To obtain the actual relative density: The output model after voxelization calculation is shown below. Figure 10 ; Step 2: Local probability calculation: A three-dimensional sliding window is constructed in the three-dimensional binary voxel matrix obtained in step one. Each local region is divided, and the ratio of the number of entity voxels in the neighborhood to the total number of voxels is calculated for each voxel point to obtain the local probability distribution. The calculation formula is as follows: ,in, The number of entity voxels within the 3D sliding window. Given the total number of elements in the 3D sliding window, the local probability distribution is mapped back to 3D space, and thresholding is performed only on the entity region to construct a 3D local probability field distribution map, see [link to map]. Figure 11 The local probability values ​​of the porous lattice structure are mainly concentrated in the middle range (about 0.2~0.5), and the color distribution is mainly green. There are no obvious high value (red) or low value (blue) areas. This phenomenon indicates that there are no obvious pure solid areas or pure porous areas in the structure. Instead, it presents a spatial distribution feature of continuous transition between solid and porous areas. Compared with the traditional rod-shaped lattice structure, the porous lattice structure has a more uniform and smooth local probability distribution due to its continuous curved surface characteristics, reflecting its excellent structural uniformity and isotropic characteristics. Step 3: Calculate the entropy value of each local region: Based on the probability distribution obtained in step two, and using the information entropy formula, the entropy value of each local region is calculated: ,in, For entity voxel probability, The probability of a pore voxel; Step 4: Construct a three-dimensional local entropy field: A three-dimensional local entropy field is constructed based on the entropy values ​​of each local region calculated in step three. That is, based on the information entropy formula, the local entropy value of each voxel position is calculated. By mapping the entropy value to three-dimensional space, a local complexity distribution map of the porous structure can be obtained, which is used to characterize the degree of mixing between the solid and the pores in the local region. See Figure 12 The red area represents the high-entropy region, corresponding to the transition interface between solids and pores; the blue (low-level) area represents the low-entropy region, corresponding to pure solid or pure pore regions. This three-dimensional local entropy field map clearly depicts the interface distribution of the structure. The structure as a whole exhibits a relatively continuous and uniform high-entropy distribution, indicating that solids and pores in its local region exhibit a continuous alternating spatial distribution, unlike the situation in traditional rod-shaped lattice structures where high-entropy values ​​only appear in the boundary region. The constructed three-dimensional local entropy field can effectively characterize the local spatial complexity of continuous curved porous structures, providing a foundation for subsequent three-dimensional entropy gradient field calculation and high-gradient region extraction. Step 5: Spatial gradient calculation: The three-dimensional local entropy field constructed in step four with size (101, 101, 101) Perform spatial gradient calculation to obtain the three-dimensional local entropy gradient vector: The three-dimensional local entropy gradient vectors at all spatial locations together constitute the entropy gradient vector field, see... Figure 12 Further calculate the magnitude of the three-dimensional local entropy gradient: The three-dimensional local entropy gradient magnitudes at all spatial locations collectively constitute the entropy gradient magnitude field. Results show that the gradient components in the X, Y, and Z directions range from -0.7219278 to 0.7219278, with a minimum magnitude of 0.0, a maximum of 0.7344098, and an average of 0.1168139. Further statistical analysis of the gradient components in each direction within the solid region yields the following three-dimensional average entropy gradient vectors: The above results indicate that the local complexity of the porous lattice structure varies relatively uniformly across the three spatial directions, exhibiting significant spatial isotropic characteristics. Further mapping the entropy gradient magnitude to the solid region for three-dimensional visualization yields a three-dimensional entropy gradient magnitude distribution map, see [link to relevant documentation]. Figure 13 The entropy gradient exhibits a relatively uniform distribution across the entire continuous surface structure, effectively reflecting the spatial distribution patterns of the transition region and local change region of the surface. Step 6: Extraction of high gradient regions: Based on the spatial distribution characteristics of the three-dimensional entropy gradient magnitude field constructed in step five, high-gradient regions are extracted from the areas of drastic change in the structure. Specifically, a statistical quantile method is used to set a high-gradient threshold, with the 90th quantile of the entropy gradient magnitude within the solid region as the criterion. When the voxel position satisfies: At that time, the voxel was identified as a high gradient region, in which The threshold value is set; through statistical analysis of the entropy gradient magnitude within the entity region, the threshold value is determined as follows: Under this threshold condition, the number of voxels extracted from the high gradient region is 30291, and the total number of entity voxels is 302851. Further calculation yields the volume fraction of the high gradient region as follows: The results show that high-gradient regions account for approximately 10% of the solid structure, indicating that only a small portion of the structure exhibits significant complexity changes; this can be seen through 3D visualization. Figure 15 The high gradient region is mainly distributed in the location of severe bending of the structural surface and the region of abrupt geometric change in the channel. It can effectively characterize the key region in the structure where the local complexity changes significantly. The result shows that the entropy gradient-based method can automatically identify the region of severe structural change from complex continuous porous structure without human intervention, providing an important basis for structural optimization design and performance analysis. Step 7: Feature Construction and Application After constructing the three-dimensional local entropy field and entropy gradient field and extracting high-gradient regions in the aforementioned steps, the porous structure is further characterized to form a multi-dimensional feature vector that can be used for engineering analysis and machine learning modeling. Statistical analysis is then performed on the three-dimensional local entropy field within the solid region to calculate the average entropy value and entropy standard deviation. The average entropy value characterizes the overall spatial complexity of the structure, while the entropy standard deviation reflects the dispersion of the structural complexity. The calculated average entropy value is: The standard deviation of entropy is: Furthermore, the components of the entropy gradient vector field and the entropy gradient magnitude field in the three spatial directions are statistically analyzed to obtain the average gradient values ​​in each direction, which are used to characterize the directional features of structural complexity changes, resulting in: The results show that the average gradient values ​​of the porous structure are basically consistent in the X, Y, and Z directions, indicating that its local complexity variation has good spatial uniformity, reflecting the isotropic characteristics of a continuous curved surface porous structure. Furthermore, statistical analysis of the entropy gradient magnitude reveals that the maximum gradient value is: This value corresponds to the location of the most dramatic changes in local complexity within the structure, typically situated in areas with pronounced surface transitions, channel contractions, or expansions. This allows for a quantitative description of the intensity and spatial distribution of local complexity changes within the structure. Furthermore, based on the high-gradient regions extracted in step six, their volume fraction within the solid region is calculated. The volume fraction of the high-gradient regions is: This indicates that approximately 10.00% of the region in the structure belongs to the region of significant complexity change, suggesting that only a small portion of the region bears the main local complexity change; in summary, the constructed multidimensional feature vector is: The feature vector corresponds to the average entropy value, entropy standard deviation, average gradient in the X direction, average gradient in the Y direction, average gradient in the Z direction, maximum gradient value, and volume fraction of high gradient region, respectively. This feature vector can comprehensively characterize porous structures from multiple perspectives such as overall complexity, spatial non-uniformity, directional variation, and degree of local mutation. It can be used as input for machine learning models for engineering applications such as prediction of the mechanical properties of porous structures, structural optimization design, and identification of failure-sensitive areas.

[0056] In this embodiment, the voxel size of the voxelization process is adaptively set according to the feature size of the porous structure to achieve a balance between structural detail representation and computational efficiency. The minimum feature size of the structure is the diameter of the rod, which is about 0.5 mm. The voxel size is selected as 0.1 mm, and the corresponding voxel matrix size is (101,101,101). This voxel size is about 1 / 10 of the structural feature scale, which can effectively control the computational scale while ensuring the accurate representation of the continuous curved surface morphology of the structure.

[0057] In this embodiment, the three-dimensional sliding window adopts a cube window form, and local probability statistics are performed on the 5×5×5 three-dimensional sliding window to obtain the three-dimensional local probability field. The calculation results show that the range of values ​​for the local probability field is: The average value is: This average value is compared with the entity voxel probability obtained in step one. The results are largely consistent, verifying the correctness and stability of the local probability calculation.

[0058] In this embodiment, the three-dimensional local entropy field is constructed by mapping the entropy value corresponding to the center position of the three-dimensional sliding window to the three-dimensional space. The entropy field is calculated through the local probability distribution, and its value ranges from 0 to 0.99995387, with an average entropy value of 0.22771609. The results show that the gyroid structure as a whole has high local complexity, and the entropy field exhibits continuous distribution characteristics in space.

[0059] In this embodiment, the spatial gradient is calculated using the finite difference method, with the central difference method employed to improve calculation accuracy. By calculating the gradient of the entropy field, the gradient components in each direction are obtained to have a range of -0.7219278. The maximum gradient magnitude is 0.7219278, and the average value is 0.7344098. The results show that the complexity of the structure varies in the three spatial directions in a basically consistent manner, which reflects the good isotropic characteristics of the continuous curved surface porous structure.

[0060] In this embodiment, when constructing the multidimensional feature vector, it is fused with geometric parameter features, that is, by further combining geometric parameters such as the relative density of the structure (0.2939442), a complete multidimensional feature description system can be formed, thereby significantly improving the comprehensive characterization ability of porous structures.

[0061] In this embodiment, the method is applicable to various types of porous structures, including solid rod lattice structures, hollow rod lattice structures, and continuous curved surface structures. The porous lattice structure used in this embodiment is a typical three-period minimal surface (TPMS) structure, which verifies that the method also has good applicability to continuous complex porous structures.

[0062] In this embodiment, the multidimensional structural feature vector can be used as input data for machine learning model training to achieve performance prediction of porous structures. The models include support vector machines, random forests, XGBoost, and neural networks. By establishing a mapping relationship between structural features and mechanical properties, efficient prediction of properties such as elastic modulus, strength, and energy absorption can be achieved.

[0063] In this embodiment, the method can also be used to identify local non-uniform regions or potential failure regions in porous structures. The volume fraction of high gradient regions is 0.100019, which means that about 10% of the structural region bears the main complexity changes. By analyzing such regions, the location of possible stress concentration in the structure can be effectively identified, thereby providing an important basis for structural optimization design.

[0064] Through the above embodiments, the present invention not only achieves high-precision three-dimensional characterization of the complexity of porous structures, but also quantitatively describes the directional characteristics and local mutation characteristics of the structure, significantly enhancing the engineering application value of the method in the design and performance prediction of porous structures in additive manufacturing.

[0065] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Any simple modifications, alterations, and equivalent changes made to the above embodiments based on the inventive essence shall still fall within the protection scope of the present invention.

Claims

1. A method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling, characterized in that, The method includes the following steps: Step 1: 3D structure voxelization: A three-dimensional model of the porous structure is obtained, and the three-dimensional model is voxelized to obtain a three-dimensional binary voxel matrix. The voxel value is either solid or pore, with solid parts assigned a value of 1 and pore parts assigned a value of 0. Step 2: Local probability calculation: A three-dimensional sliding window is constructed in the three-dimensional binary voxel matrix obtained in step one. Each local region is divided, and the probability distribution of solid voxels and pore voxels in each local region is statistically analyzed. Step 3: Calculate the entropy value of each local region: Based on the probability distribution obtained in step two, and using the information entropy formula, the entropy value of each local region is calculated: ;in, For entity voxel probability, The probability of a pore voxel; Step 4: Construct a three-dimensional local entropy field: A three-dimensional local entropy field is constructed based on the entropy values ​​of each local region calculated in step three. ; Step 5: Spatial gradient calculation: The three-dimensional local entropy field constructed in step four Perform spatial gradient calculation to obtain the three-dimensional local entropy gradient vector: The three-dimensional local entropy gradient vectors at all spatial locations together constitute the entropy gradient vector field. Further calculations are performed on the magnitude of the three-dimensional local entropy gradient. The magnitudes of the three-dimensional local entropy gradients at all spatial locations collectively constitute the entropy gradient magnitude field; among them, , and Let X, Y, and Z represent the gradient components of the local entropy field in the X, Y, and Z directions, respectively. This represents the overall intensity of local entropy changes; Step 6: Extraction of high gradient regions: Based on the spatial distribution characteristics of the three-dimensional entropy gradient magnitude field constructed in step five, high-gradient regions are extracted from the drastically changing areas in the structure. A statistical quantile method is used to set a high-gradient threshold, where the voxel position satisfies the following conditions: At that time, the voxel was identified as a high gradient region, in which The volume fraction of the high gradient region is calculated under the given threshold. Step 7: Feature Construction and Application The three-dimensional local entropy field constructed in step four, the entropy gradient vector field and entropy gradient magnitude field constructed in step five, and the volume fraction of the high gradient region obtained in step six are used to construct a multi-dimensional feature vector as a feature description of the porous structure, which is used for structural optimization analysis or performance prediction.

2. The method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling according to claim 1, characterized in that, The porous structure mentioned in step one includes solid rod structure, hollow rod structure, and regular or irregular lattice structure.

3. The method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling according to claim 1, characterized in that, The voxel size in the voxelization process described in step one is set according to the characteristic size of the porous structure, specifically 1 / 5 to 1 / 10 of the structural characteristic size. This structural characteristic size is the smallest characteristic scale in the porous structure, including the diameter of the rod, the pore diameter, or the smallest unit cell size.

4. The method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling according to claim 1, characterized in that, The three-dimensional sliding window mentioned in step two is a cube window with a size of n×n×n, where n is an integer greater than or equal to 3.

5. The method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling according to claim 1, characterized in that, The three-dimensional local entropy field described in step four is constructed by mapping the entropy value corresponding to the center position of the three-dimensional sliding window to three-dimensional space.

6. The method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling according to claim 1, characterized in that, The spatial gradient calculation described in step five is performed using the finite difference method, including central difference or forward difference.

7. The method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling according to claim 1, characterized in that, The three-dimensional local entropy value and its gradient-related component values ​​mentioned in step five include the average entropy value, entropy standard deviation, average gradient in the X direction, average gradient in the Y direction, average gradient in the Z direction, and maximum gradient value.

8. The method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling according to claim 1, characterized in that, In step six, the multidimensional feature vector is fused with geometric parameter features; the geometric parameter features include relative density, porosity, specific surface area, and rod dimensions.

9. The method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling according to claim 1, characterized in that, The multidimensional feature vectors are used for machine learning model training to predict the mechanical properties of porous structures.

10. The method for constructing three-dimensional local entropy gradient features of porous structures for machine learning modeling according to claim 1, characterized in that, This method is used to identify localized non-uniform regions or potential failure regions in porous structures.

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