Hexahedral mesh intelligent simplification method capable of guaranteeing analysis precision

Abstract

The invention discloses a hexahedral mesh intelligent simplification method with guaranteed analysis precision, and belongs to the technical field of hexahedral mesh simplification, and the method comprises the following steps: 1, carrying out the feature extraction of layers and columns of a hexahedral mesh, including geometric features, topological features, quality features and physical features; step 2, carrying out validity check on the layers and the columns; 3, predicting the deletion probability of a deletable layer / column based on the constructed simplified neural network HSimNet; and step 4, executing layer / column deletion operation. According to the method, physical characteristics of layers and columns are introduced into hexahedral mesh simplification for the first time, model simplification is associated with physical problems, geometric characteristics are introduced into hexahedral mesh simplification, and layer and column structures causing geometric ineffectiveness of the mesh are pre-judged, so that geometric effectiveness of the simplified mesh is guaranteed; topological features and quality features are introduced into hexahedral mesh simplification, so that the overall quality of the simplified mesh is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of hexahedral mesh simplification, and particularly relates to an intelligent hexahedral mesh simplification method for preserving analysis accuracy. Background Art

[0002] In finite element analysis, hexahedral meshes have significant advantages over other volume meshes in terms of computational speed, convergence speed, and storage space due to their good hierarchical structure, and are thus considered ideal finite element volume meshes. Currently, the main method for generating hexahedral meshes is to generate uniform hexahedral meshes. However, in actual simulation analysis, due to the existence of stress non-concentrated areas and stress concentrated areas under the same mesh granularity, it will lead to waste of computational cost and memory resources.

[0003] In order to improve the accuracy and efficiency of numerical analysis, many researchers have proposed structural simplification methods for hexahedral meshes. Due to the global nature of the hexahedral mesh structure, common simplification operations only include layer deletion and column deletion operations. Currently, the main focus of hexahedral mesh simplification methods is on determining the layers and columns to be deleted and optimizing the deletion order.

[0004] In traditional hexahedral mesh simplification methods, some people determine the layer structure to be deleted by defining the dilation and compression metrics of layers to control the overall density of the mesh. Some people use the method of uniformly deleting the original layer structure and determine all the layers to be deleted at once based on topological quality prediction, and perform layer set deletion operations to obtain the optimized block structure of the mesh. In order to optimize the topological structure during the mesh simplification process, some people use Euler characteristics, manifoldness, edge valence, boundary conformity, etc. as the criteria for deleting layer and column structures, and heuristically perform deletion operations according to the widths of layers and columns, and check the mesh validity to obtain the simplified hexahedral mesh. In order to further optimize the block structure, some people propose a weighted layer and column deletion sorting algorithm by considering the change in the topological quality of the mesh after layer and column deletion.

[0005] In recent years, with the wide application of mesh data in multiple fields and the large amount of characteristic information contained in the mesh itself, it has become a powerful resource for training data of artificial intelligence models. Therefore, the research in the field of intelligent mesh generation and processing has also increased day by day. Some people have proposed a triangle mesh simplification method based on neural networks, which captures mesh features through an attention mechanism and uses a neural network to optimize the Hausdorff distance between the simplified mesh and the original input mesh to determine the optimal vertex merging position, thus achieving efficient mesh simplification; some people have learned the mesh connection distribution through an attention mechanism and constructed a mesh simplification model based on graph neural meshes.

[0006] In summary, the traditional hexahedral mesh simplification method does not consider the actual physical analysis results and cannot associate the mesh structure characteristics with the analysis accuracy. Therefore, the simplification effect of some hexahedral meshes is not ideal.

[0007] Based on this, the present invention designs an intelligent hexahedral mesh simplification method that preserves analysis accuracy to solve the above problems. Summary of the Invention

[0008] The purpose of the present invention is to propose an intelligent hexahedral mesh simplification method that preserves analysis accuracy to solve the problems in the above background technology.

[0009] To achieve the above purpose, the present invention adopts the following technical solutions:

[0010] An intelligent hexahedral mesh simplification method that preserves analysis accuracy includes the following steps:

[0011] Step 1: Extract the characteristics of the layers and columns of the hexahedral mesh, including geometric characteristics, topological characteristics, quality characteristics, and physical characteristics:

[0012] 1) Define the layer / column geometric characteristics according to the geometric attributes of the boundary point pairs to be merged during the layer / column deletion process;

[0013] 2) Define the layer / column topological characteristics by calculating the number of hexahedral elements included in the layer / column and the predicted change value of the local topological quality after the layer / column deletion;

[0014] 3) Define the layer / column quality characteristics according to the Jacobian ratio and shear distortion of the hexahedral elements;

[0015] 4) Define the layer / column physical characteristics through the strain values of each mesh vertex;

[0016] Step 2: Check the validity of the layers and columns:

[0017] 5) Avoid generating poor local structures that cannot be repaired by geometric optimization by establishing geometric constraints and topological constraints;

[0018] Step 3: Based on the constructed simplification neural network HSimNet, predict the deletion probability of the deletable layers / columns:

[0019] 6) Construct the HSimNet network architecture through the neural network and predict the deletion probability of the deletable layers / columns;

[0020] Step 4: Perform the layer / column deletion operation:

[0021] 7) If the maximum deletion probability is higher than the deletion threshold, perform a deletion operation on this layer or column, and go back to step one to update the layer and column features; if the deletion probabilities of all layers and columns are less than the deletion threshold, the simplification termination condition is reached, and the simplified grid is output.

[0022] As a further description of the above technical solution: in the layer / column geometric features, the geometric attributes of the boundary point pairs to be merged in the layer / column are put into a matrix, where the geometric attribute entity of each boundary grid point is either pi (the i-th geometric point), or cj (the j-th geometric edge), or fk (the k-th geometric face), and the layer / column geometric attribute matrix is constructed as the geometric feature of the layer / column.

[0023] As a further description of the above technical solution: the specific steps for defining the layer / column topological features by calculating the number of hexahedron elements contained in the layer / column and the change value of the local topological quality after predicting the deletion of the layer / column are as follows:

[0024] (1) Determine the number of hexahedron elements contained in the layer / column: By traversing the hexahedrons of each layer / column, determine the number of hexahedrons contained in this layer / column;

[0025] (2) Determine the initial grid topological quality and the ideal grid topological quality: The grid topological quality can be defined based on the degree of the grid edge: where V e represents the degree of the grid edge e, that is, the number of adjacent grid faces, and VI e represents the ideal degree of the grid edge e. The ideal degree of the grid edge is affected by its geometric attribute: If this grid edge is an internal grid edge, its ideal degree should be VI e = 4; if this grid edge is located on a geometric face, its ideal degree is VI e = 3; if this grid edge is located on a geometric edge, its ideal degree should be determined according to the dihedral angle of the geometric edge where α is the dihedral angle degree of the geometric edge;

[0026] (3) Determine the change value of the local topological quality after layer deletion: For layer s, its grid edges can be divided into two categories. One category is the grid edges to be deleted, such as es, and the other category is the grid edge pairs to be merged, such as (ec1, ec2). The degree of the grid edge after the merging of the to-be-merged edge pairs is:

[0027]

[0028] The ideal degree of the merged grid edge is The change value of the local topological quality after layer deletion is

[0029]

[0030] (4) Determine the change value of the local topological quality after column deletion: For column c, its mesh edges can be divided into three categories. One category is the pair of mesh edges parallel to the column that need to be merged, such as (eh1, eh2). Another category is the pair of mesh edges perpendicular to the column that need to be merged, such as (ev1, ev2). The third category is the pair of mesh edges whose adjacency structure changes, such as en1 and en2. The degree of the mesh edge after merging the pair of mesh edges parallel to the column is: is:

[0031]

[0032] The degree of the mesh edge after merging the pair of mesh edges perpendicular to the column is:

[0033]

[0034] The degree of the mesh edge whose adjacency structure changes is: The local topological quality after column deletion: Since the local topological quality of the mesh before column deletion is The change in the mesh topological quality is

[0035] As a further description of the above technical solution: The process of extracting the layer / column quality characteristics is as follows:

[0036] (1) Determine the maximum and average shearing degrees of the layer / column: For a hexahedral mesh, the face shearing degree refers to the normalized value of the shearing angle of the quadrilateral face with parallel topology inside the hexahedral element:

[0037] where d p1 and d p2 are the perpendicular distances from the center points of two quadrilateral faces to the opposite face, d is the distance between the center points of the quadrilateral face, and the element shearing degree is defined as the maximum value of the shearing degrees of the three faces contained in a hexahedral element, that is, S H = max(S qp1 , S qp2 , S qp3 ), the maximum shearing degree refers to the maximum value of the shearing degrees of the corresponding volume meshes in the layer / column, that is:

[0038] S max = max{S Hi | i = 1, 2,..., n v}, the average shearing degree refers to the average value of the shearing degrees of the faces contained in the corresponding volume meshes in the layer / column, that is, S avg = avg{S Hi | i = 1, 2,..., n H}, where n H is the number of entities;

[0039] (2) Calculate the Jacobian ratio using the method in [Zhu et al. 2014 Direct Editing on Hexahedral Mesh through Dual Operations].

[0040] As a further description of the above technical solution: The process of extracting the physical characteristics of layers / columns is as follows: Obtain the strain values of each vertex of the layer and column, calculate its maximum strain value and average strain value as the physical characteristics of the layer and column. For each vertex Vsi of the layer, we assign the strain value attribute denoted as Usi, and calculate its maximum strain value and average strain value to obtain the physical characteristics as where n s is the number of vertices contained in the layer. For each vertex Vci of the column, we assign the strain value attribute denoted as Uci, and calculate its maximum strain value and average strain value to obtain the physical characteristics as where n c is the number of vertices contained in the column.

[0041] As a further description of the above technical solution: The process of establishing the geometric constraints and topological constraints is as follows:

[0042] (1) Establishment of geometric constraints: Deleting inappropriate layer and column structures will lead to geometric invalidity of the mesh. In a hexahedral mesh, geometric invalidity may cause inaccuracies, stability problems, and errors during numerical simulation, affecting the analysis accuracy. Therefore, it is crucial to ensure that there are no geometric invalid rows in the geometric model to guarantee the accuracy and reliability of the simulation and avoid potential consequences. This invalidity discrimination can be determined by the geometric attributes of boundary point pairs, that is, it can be determined by the geometric characteristics of layers / columns;

[0043] (2) Establishment of topological constraints: If an internal mesh edge with a degree less than 3 is generated after deleting a certain layer or column, that is, a doublet cell is generated, then that layer or column cannot be deleted; if after deleting a certain layer or column, it results in three vertices of a certain mesh face being on the same geometric edge, then that layer or column cannot be deleted.

[0044] As a further description of the above technical solution: The process of constructing the HSimNet network architecture:

[0045] (1) Construct a dataset according to the selected features. We randomly divide the training set and the validation set in a ratio of 80%, 20%. After obtaining the training set, we extract the feature information from it and generate a training file in the order of the features. The training file is used for sample learning;

[0046] (2) Standardize the dataset and convert the data to a standard normal distribution. We calculate the mean and standard value of each feature, and through where Z is the value after standardization, X is the original value, μ is the mean of the original value, and σ is the standard deviation of the original value;

[0047] (3) Select appropriate hyperparameters. Select the number of input layers as 8, the number of the first hidden layer as 30, the number of the second hidden layer as 12, and the learning rate as 0.001;

[0048] (4) Select an optimizer, a loss function, and an activation function. Adopt the Stochastic Gradient Descent (SGD) optimizer, and select the Mean Squared Error (MSE) as the loss function, and select relu as the activation function;

[0049] (5) Establish a neural network prediction model and test the prediction accuracy. When observing a low prediction accuracy, we perform an iterative process, go back to the first step to correct the features, and continuously adjust the model until the desired prediction accuracy level is achieved.

[0050] As a further description of the above technical solution: in the layer / column deletion operation, the layer deletion operation realizes the deletion of the layer structure by degenerating the grid edges of the layer into grid points. The column deletion realizes the deletion of the column structure by merging the diagonal grid points in the grid surface of the column and degenerating the grid surface into grid edges. Through the trained HSimNet network, predict the layer / column with the highest probability of deletion for deletion. If the maximum deletion probability is higher than the deletion threshold, perform the deletion operation on this layer or column, and go back to step one to update the layer and column features; if the deletion probabilities of all layers and columns are less than the deletion threshold and the simplification termination condition is reached, output the simplified grid.

[0051] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0052] 1. In the present invention, layers and columns are used as the basic objects for grid simplification, and the layer and column structures are comprehensively measured from multiple dimensions including geometry, topology, quality, and physics, providing rich structural features for the construction of the grid intelligent simplification model. By introducing machine learning algorithms, automatically learn the influence relationship between the hexahedral grid layer and column structures and the grid analysis accuracy from the training data, construct an intelligent simplification model for the hexahedral grid structure, and realize the simplification of the hexahedral grid while maintaining the analysis accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flowchart of an intelligent hexahedral grid simplification method for maintaining analysis accuracy proposed by the present invention;

[0054] Figure 2The following is the effect diagram of the simplification method for a hexahedral mesh intelligent simplification method that preserves analysis accuracy proposed by the present invention, where Figure 2 a is a dense hexahedral mesh and the analysis result; Figure 2 b is the input hexahedral mesh and the analysis result, Figure 2 c is the result mesh and the analysis result obtained by using the simplification method of the present invention. Specific implementation manner

[0055] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0056] Please refer to the attached Figure 1 - attached Figure 2 , the present invention provides a technical solution: a structure-guided hexahedral mesh geometry optimization method, including the following steps:

[0057] Step 1: Extract features of the layers and columns of the hexahedral mesh, including geometric features, topological features, quality features, and physical features;

[0058] Step 2: Check the validity of the layers and columns;

[0059] Step 3: Based on the constructed simplified neural network HSimNet, predict the deletion probability of the layers / columns that can be deleted;

[0060] Step 4: Perform the layer / column deletion operation;

[0061] The main process of simplifying the hexahedral mesh by using the simplification method of the present invention is as Figure 1 shown: Input the hexahedral mesh (with mesh vertex strain values and geometric models), extract features, check the validity of layers / columns, predict the maximum deletion probability of layers / columns, determine whether the simplification condition is met, and output the simplified hexahedral mesh.

[0062] An intelligent method for hexahedral meshes that preserves analysis accuracy according to the present invention introduces neural network technology. By extracting the geometric, mesh topology, quality, and physical features of the volume mesh, the powerful fitting ability of the neural network is used to effectively learn the influence of the mesh topology on the analysis accuracy, enabling it to accurately predict the topological behavior that has the least impact and accurately determine the deletion order of layers and columns. The input of the method is the hexahedral mesh and its strain analysis result, and the output is the hexahedral mesh that maintains the analysis accuracy after simplification.

[0063] In order to obtain the input feature vectors of the HSimNet model, it is first necessary to extract features in multiple aspects for each layer and each column on the input hexahedral mesh, and a feature matrix needs to be established for each layer / column.

[0064] The layer / column feature matrix is obtained in four steps: First, determine the geometric features of each layer / column according to the geometric attributes of each boundary grid vertex, then determine the topological features of each layer / column according to the mesh topology quality, then obtain the quality features of each layer / column according to the shearing degree and Jacobian ratio in the mesh quality, and finally determine the physical features of each layer / column according to the input strain analysis results.

[0065] With the help of the geometric model, the geometric attributes of each boundary grid vertex can be obtained by using the ACIS library. The geometric attribute entity of each boundary grid point is either pi (the i-th geometric point), or cj (the j-th geometric edge), or fk (the k-th geometric face). Add the geometric attributes of each vertex in the layer / column to a matrix as the geometric features of the layer / column.

[0066] After determining the geometric features, we need to represent the topological features in two dimensions: the number of hexahedral elements contained in the layer / column and the predicted change value of the local topological quality after deleting the layer / column. The number of hexahedral elements contained in the layer / column is to mark each hexahedron, obtain the hexahedral elements marked as belonging to this layer / column, and calculate their number. The predicted change value of the local topological quality after deleting the layer / column can be calculated according to the following steps:

[0067] (1) Determine the initial mesh topology quality and the ideal mesh topology quality: The mesh topology quality can be defined based on the degree of the mesh edge: where V e represents the degree of the mesh edge e, that is, the number of adjacent mesh faces, and VI e represents the ideal degree of the mesh edge e. The ideal degree of the mesh edge is affected by its geometric attributes: If the mesh edge is an internal mesh edge, its ideal degree should be VI e = 4; if the mesh edge is located on the geometric face, its ideal degree is VI e = 3; if the mesh edge is located on the geometric edge, its ideal degree should be determined according to the dihedral angle of the geometric edge where α is the dihedral angle degree of the geometric edge.

[0068] (2) Determine the change value of the local topological quality after deleting the layer: For layer s, its mesh edges can be divided into two categories. One category is the mesh edges to be deleted, such as es, and the other category is the mesh edge pairs to be merged, such as (ec1, ec2). The degree of the mesh edge after merging the to-be-merged edge pairs is:

[0069]

[0070] The merged mesh edges have an ideal degree of The local topological quality after layer deletion The change value is

[0071]

[0072] (3) Determine the change value of the local topological quality after column deletion: For column c, its mesh edges can be divided into three categories. One category is the pairs of parallel mesh edges to the column that need to be merged, such as (eh1, eh2). Another category is the pairs of perpendicular mesh edges to the column that need to be merged, such as (ev1, ev2). The third category is the pairs of mesh edges with changed adjacency structures, such as en1 and en2. The mesh edges after merging the pairs of parallel mesh edges to the column have a degree of:

[0073]

[0074] The mesh edges after merging the pairs of perpendicular mesh edges to the column have a degree of:

[0075]

[0076] The degree of the mesh edges with changed adjacency structures is: The local topological quality after column deletion: Since the local topological quality of the mesh before column deletion is The change in the mesh topological quality is

[0077] Mesh quality is a key factor affecting the analysis accuracy. To ensure the analysis accuracy, after determining the topological features, we need to determine its quality features in four dimensions: the maximum and average shearing degrees of the hexahedral elements in the layer / column, and the minimum and average Jacobian ratios of the hexahedral elements in the layer / column. The layer / column quality features can be obtained by following these steps:

[0078] (1) Determine the maximum and average shearing degrees of the layer / column: For a hexahedral mesh, the face shearing degree refers to the normalized value of the shearing angle of the quadrilateral face parallel to the topology within the hexahedral element: where d p1 and d p2 are the perpendicular distances from the center points of two quadrilateral faces to the opposite face, and d is the distance between the center points of the quadrilateral face. The element shearing degree is defined as the maximum value of the shearing degrees of the three faces contained within a hexahedral element, i.e., S H = max(S qp1 , S qp2 , S qp3)。The maximum shearing degree refers to the maximum shearing degree of the corresponding volume meshes in a layer / column, that is: S max = max{S Hi | i = 1, 2,..., n v}}. The average shearing degree refers to the average shearing degree of the faces contained in the corresponding volume meshes in a layer / column, that is S avg = avg{S Hi | i = 1, 2,..., n H}}, where n H is the number of volumes.

[0079] (2) Calculate the Jacobian ratio. The method in [Zhu et al. 2014 Direct Editing on Hexahedral Mesh through Dual Operations] is used for calculation.

[0080] After determining the quality characteristics, in order to be able to explicitly express the influence relationship between the mesh structure and quality of different strain regions on the analysis accuracy, we use two dimensions to represent the physical characteristics, obtain the strain values of each vertex of the layer and column, and calculate its maximum strain value and average strain value as the physical characteristics of the layer and column. For each vertex Vsi of the layer, we assign the strain value attribute denoted as Usi, and calculate its maximum strain value and average strain value to obtain the physical characteristics as where n s is the number of vertices contained in the layer. For each vertex Vci of the column, we assign the strain value attribute denoted as Uci, and calculate its maximum strain value and average strain value to obtain the physical characteristics as where n c is the number of vertices contained in the column.

[0081] In order to be able to perform validity checks on the layer and column, we use their geometric characteristics and topological structure to establish geometric constraints and topological constraints. In order to avoid geometric invalid situations during the mesh simplification process, we determine all possible boundary points that may lead to geometric failure for geometric attributes according to the layer / column deletion method and geometric characteristics, as shown in Table 1. In order to avoid poor local structures that cannot be repaired through geometric optimization during the layer / column deletion process, the following topological constraints are added:

[0082] (1) If it is predicted that the deletion of a certain layer or column will result in an internal mesh edge with a degree less than 3, that is, a doublet cell is generated, then this layer or column cannot be deleted;

[0083] (2) If after the deletion of a certain layer or column, it results in three vertices of a certain mesh face being on the same geometric edge, then this layer or column cannot be deleted;

[0084] In order to enable the network to better learn the impact of the topological changes of the grid on the analysis accuracy during the grid simplification process, we need to select a suitable network model for construction. The following are the specific steps for building the network model:

[0085] (1) Construct a dataset based on the selected features. We randomly divide the training set and the validation set in the ratio of 80% and 20%. After obtaining the training set, we extract the feature information from it and generate a training file according to the order of the features. The training file is used for sample learning.

[0086] (2) Standardize the dataset. Convert the data into a standard normal distribution. We calculate the mean and standard value of each feature, and through where Z is the value after standardization, X is the original value, μ is the mean of the original value, and σ is the standard deviation of the original value.

[0087] (3) Select appropriate hyperparameters. Select the number of input layers to be 8, the number of the first hidden layer to be 30, the number of the second hidden layer to be 12, and the learning rate to be 0.001.

[0088] (4) Select an optimizer, a loss function, and an activation function. Adopt the Stochastic Gradient Descent (SGD) optimizer and select the Mean Squared Error (MSE) as the loss function. Select relu as the activation function.

[0089] (5) Establish a neural network prediction model and test the prediction accuracy. When observing a low prediction accuracy, we perform an iterative process, return to the first step to correct the features, and continuously adjust the model until the desired prediction accuracy level is achieved.

[0090] For the deletable layers / columns that pass the pre-judgment, calculate the deletion probability using HSimNet according to their topology, quality, and physical characteristics.

[0091] The layer deletion method for step 4) selected adopts [Borden MJ et al 2002 Coarsening and sheet extraction for all - hexahedral meshes.]. Column deletion is achieved by merging the diagonal grid points in the grid faces of the column, degenerating the grid face into a grid edge, thus realizing the deletion of the column structure. Traverse all deletable layers / columns, determine the layer i with the highest deletion probability, perform the deletion operation on it, and optimize the local grid using the local Laplace geometric optimization method; update the characteristics of the affected layers / columns for the simplified grid, and iterate to simplify the grid according to the above steps until the termination condition is met. In the feature update stage of the simplified grid, only update the characteristics of the layers / columns adjacent to or intersecting with the deleted layer / column, where the geometric, topological, and quality characteristics are recalculated, and the strain value of the newly generated grid vertex v' is the average of the strain values of the two original grid vertices merged into this vertex. where u' is the strain value of the newly generated grid vertex, u i and u j are the two vertices merged into v' during layer / column deletion. When the simplified grid meets one of the following two conditions, the grid simplification terminates: 1) All layers and columns of the simplified grid are non - deletable layers / columns; 2) The deletion probabilities of all deletable layers / columns of the simplified grid are lower than 96%.

[0092] For the simplified grid, the linear interpolation method is used to solve the true solution of each vertex. For each grid vertex v, first determine which hexahedral element in the grid H this point is located in, and then use barycentric coordinate interpolation to obtain the true solution of vertex v according to the true solutions of the vertices of this hexahedral element. For each vertex v of the grid before and after simplification i The relative error of the displacement value is where u i is the actual strain - displacement value of grid vertex v i , and

[0093] As Figure 2 shown, it is the comparison diagram of the hexahedral grid simplification results obtained by the simplification method proposed in the present invention. Figure 2 a is the dense hexahedral grid and the analysis result; Figure 2 b is the input hexahedral grid and the analysis result, the minimum Jacobian ratio is 0.73, the average Jacobian ratio is 1.0, the maximum relative error is 3.07%, and the average relative error is 0.45%; Figure 2 c is the result grid and the analysis result obtained by using the simplification method of the present invention, the lowest Jacobian ratio is 0.28, the average Jacobian ratio is 0.86, the maximum relative error is 2.05%, and the average relative error is 0.82%; From Figure 2As can be seen from the simplification effect, the simplification method of the present invention can not only significantly reduce the number of grid cells, but also generally maintain the analysis accuracy of the model, achieving hexahedron mesh simplification with accuracy preservation.

[0094] The above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, making equivalent substitutions or changes should be covered within the protection scope of the present invention.

Claims

1. A hexahedral mesh intelligent simplification method that maintains analysis accuracy, characterized in that: The following steps are involved: Step 1: Extract features from the layers and columns of the hexahedral mesh, including geometric features, topological features, quality features, and physical features: 1) Define the layer / column geometric features according to the geometric properties of the boundary point pairs to be merged during the layer / column deletion process; 2) defining the layer / column topological features by calculating the number of hexahedral units contained in the layer / column and the predicted change in local topological quality after the layer / column is deleted; 3) Define layer / column quality characteristics based on the Jacobian value and shear of the hexahedral element; 4) Define the layer / column physical characteristics through the strain value of each mesh vertex; Step 2: Check the validity of layers and columns: 5) By establishing geometric constraints and topological constraints, we can avoid the generation of poor local structures that cannot be repaired by geometric optimization; Step 3: Based on the constructed simplified neural network HSimNet, predict the deletion probability of the deletable layers / columns: 6) Through neural networks, build the HSimNet network architecture and predict the deletion probability of deletable layers / columns; Step 4: Execute layer / column deletion operation: 7) If the maximum deletion probability is higher than the deletion threshold, the deletion operation is performed on the layer or column, and the process returns to step 1 to update the layer and column features. If the deletion probabilities of all layers and columns are less than the deletion threshold, the simplification termination condition is reached, and the simplified grid is output.

2. The intelligent simplification method for hexahedral meshes with guaranteed analysis accuracy according to claim 1, characterized in that: In the layer / column geometric features, the geometric attributes of the boundary point pairs to be merged in the layer / column are placed in a matrix, where the geometric attribute entity of each boundary grid point is either pi (the i-th geometric point), cj (the j-th geometric edge), or fk (the k-th geometric face), and a layer / column geometric attribute matrix is ​​constructed as the geometric features of the layer / column.

3. The intelligent simplification method for hexahedral meshes with guaranteed analysis accuracy according to claim 1, characterized in that: The specific steps of defining the layer / column topological features by calculating the number of hexahedral units contained in the layer / column and the predicted change value of the local topological quality after the layer / column is deleted are as follows: (1) Determine the number of hexahedral units contained in a layer / column: Determine the number of hexahedral units contained in each layer / column by traversing the hexahedrons in the layer / column; (2) Determine the initial mesh topology quality and the ideal mesh topology quality: The mesh topology quality can be defined based on the degree of the mesh edge: Where V e represents the degree of the mesh edge e, that is, the number of adjacent mesh faces, VI e The ideal degree of the mesh edge e is affected by its geometric properties: if the mesh edge is an internal mesh edge, its ideal degree should be VI e =4; if the mesh edge is located on the geometric surface, its ideal degree is VI e =3; if the mesh edge is located on a geometric edge, its ideal degree should be determined based on the dihedral angle of the geometric edge Where α is the dihedral angle of the geometric edge; (3) Determine the change in local topology quality after layer deletion: For layer s, its mesh edges can be divided into two categories: one is the deleted mesh edges, such as es, and the other is the mesh edge pairs that need to be merged, such as (ec1, ec2). The degree of the mesh edges after the edge pairs to be merged is: Merged mesh edges The ideal degree is Local topology quality after layer deletion The change value is (4) Determine the change in local topological quality after column deletion: For column c, its mesh edges can be divided into three categories: one is the mesh edge pairs parallel to the column that need to be merged, such as (eh1, eh2); one is the mesh edge pairs perpendicular to the column that need to be merged, such as (ev1, ev2); and one is the mesh edge pairs whose adjacency structure has changed, such as en1 and en2. The mesh edge pairs parallel to the column are merged. The degree of is: The mesh edges perpendicular to the columns are the mesh edges after merging. The degree of is: The degree of the mesh edge whose adjacency structure changes is: Local topology quality after column removal: Since the local topological quality of the mesh before deleting the column is The change in mesh topology quality is 4. The intelligent simplification method for hexahedral meshes with guaranteed analysis accuracy according to claim 1, characterized in that: The process of layer / column quality feature extraction is as follows: (1) Determine the maximum and average misalignment of layers / columns: For hexahedral meshes, the face misalignment refers to the normalized value of the misalignment angle between the parallel topological quadrilateral faces within the hexahedral unit: where d p1 and d p2 is the vertical distance from the center point of two quadrilateral faces to the opposite face, d is the distance between the center points of the quadrilateral faces, and the unit shear degree is defined as the maximum value of the shear degree of the three faces contained in a hexahedral unit, that is, S H =max(S qp1 ,S qp2 ,S qp3 ), the maximum misalignment refers to the maximum misalignment of the corresponding volume mesh in the layer / column, that is: S max =max{S Hi |i=1,2,...,n v }, the average shearing refers to the average shearing of the faces contained in the corresponding volume grid in the layer / column, that is, S avg =avg{S Hi |i=1,2,...,n H }, where n H is the number of bodies; (2) The Jacobian value is calculated using the method in [Zhu et al. 2014 Direct Editing on Hexahedral Mesh through Dual Operations].

5. The intelligent simplification method for hexahedral meshes with guaranteed analysis accuracy according to claim 1, characterized in that: The process of establishing the geometric constraints and topological constraints is as follows: (1) Geometric constraint establishment: Inappropriate deletion of layer and column structures will lead to geometric invalidity of the mesh. In a hexahedral mesh, geometrically invalid rows may cause inaccuracy in numerical simulation, stability problems and errors in the simulation process, affecting the accuracy of the analysis. Therefore, it is crucial to ensure that there are no geometrically invalid rows in the geometric model to ensure the accuracy and reliability of the simulation and avoid potential consequences. This invalidity judgment can be determined by the geometric properties of the boundary point pairs, that is, it can be determined by the geometric characteristics of the layer / column; (2) Establishment of topological constraints: If deleting a layer or column generates internal mesh edges with a degree less than 3, that is, doublet units, then the layer or column cannot be deleted; if deleting a layer or column causes the three vertices of a mesh surface to be on the same geometric edge, then the layer or column cannot be deleted.

6. The intelligent simplification method for hexahedral meshes with guaranteed analysis accuracy according to claim 1, characterized in that: The process of building the HSimNet network architecture is as follows: (1) Construct a data set based on the selected features. We randomly divide the training set and validation set into 80% and 20% ratios. After obtaining the training set, we extract feature information from it and generate a training file in the order of features. The training file is used for sample learning. (2) Standardize the data set and convert the data into a standard normal distribution. We calculate the mean and standard value of each feature. Where Z is the standardized value, X is the original value, μ is the mean of the original value, and σ is the standard deviation of the original value; (3) Select appropriate hyperparameters, select the number of input layers as 8, the number of the first hidden layer as 30, the number of the second hidden layer as 12, and the learning rate as 0.001; (4) Select the optimizer, loss function, and activation function. Use the stochastic gradient descent optimizer (SGD), select the mean square error (MSE) as the loss function, and select relu as the activation function. (5) A neural network prediction model was established and the prediction accuracy was tested. When a low prediction accuracy was observed, we performed an iterative process and returned to the first step to modify the features in order to continuously adjust the model until the desired level of prediction accuracy was achieved.

7. The intelligent simplification method for hexahedral meshes with guaranteed analysis accuracy according to claim 1, characterized in that: In the layer / column deletion operation, the layer deletion operation realizes the deletion of the layer structure by degenerating the grid edge of the layer into grid points, and the column deletion operation realizes the deletion of the column structure by merging the diagonal grid points in the grid surface of the column and degenerating the grid surface into grid edges. The trained HSimNet network predicts the maximum probability of deleting the layer / column for deletion. If the maximum deletion probability is higher than the deletion threshold, the deletion operation is performed on the layer or column, and the process returns to step 1 to update the layer and column features. If the deletion probabilities of all layers and columns are less than the deletion threshold, the simplification termination condition is reached and the simplified grid is output.

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