A method for intelligently simplifying hexahedral mesh with analysis accuracy preserved

Abstract

The application discloses a hexahedral mesh intelligent simplification method with analysis precision ensured, and belongs to the technical field of hexahedral mesh simplification, and comprises the following steps: step one, feature extraction is performed on layers and columns of the hexahedral mesh, including geometric features, topological features, quality features and physical features; step two, effectiveness checking is performed on the layers and columns; step three, based on the constructed simplification neural network HSimNet, the deletion probability of layers / columns that can be deleted is predicted; and step four, layer / column deletion operation is performed. In the application, the physical features of layers and columns are introduced in the hexahedral mesh simplification for the first time, the model simplification is connected with the physical problem, the geometric features are introduced in the hexahedral mesh simplification, the layer and column structures that cause invalid grid geometry are predicted, so that the geometric effectiveness of the simplified grid is ensured; the topological features and the quality features are introduced in the hexahedral mesh simplification, so that the overall quality of the simplified grid is ensured.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of hexahedral mesh simplification, and particularly relates to a hexahedral mesh intelligent simplification method with analysis accuracy preserved. BACKGROUND

[0002] In finite element analysis, hexahedral mesh has significant advantages in calculation speed, convergence speed and storage space compared with other volume meshes due to its good hierarchical structure, and is therefore considered as an ideal finite element volume mesh. Current hexahedral mesh generation methods mainly focus on generating uniform hexahedral meshes, but in actual simulation analysis, due to the existence of stress concentration and stress concentration areas under the same mesh granularity, the calculation cost and memory resources are wasted.

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

[0004] In traditional hexahedral mesh simplification methods, some people define the expansion and compression degrees of layers to determine the layer structure to be deleted and control the overall density of the mesh. Some people uniformly delete the original layer structure, and based on the topological quality, they determine all the layers to be deleted at one time and perform layer set deletion operation to obtain the optimized block structure of the mesh. In order to optimize the topological structure during mesh simplification, some people use Euler characteristics, manifoldness, edge valence, boundary conformity, etc. as the criteria for layer and column structure deletion, and perform deletion operation heuristically according to the width of the layer and column, and check the validity of the mesh to obtain the simplified hexahedral mesh. In order to further optimize the block structure, some people consider the topological quality changes of the mesh after layer and column deletion, and propose a weighted layer and column deletion sorting algorithm.

[0005] In recent years, with the wide application of mesh data in many fields and the large amount of characteristic information contained in the mesh itself, mesh has become a powerful resource for artificial intelligence model training data, so the research in the field of mesh intelligent generation and processing has also increased. Some people have proposed a triangular mesh simplification method based on neural network, which captures mesh features through attention mechanism, optimizes the Hausdorff distance between the simplified mesh and the original input mesh using neural network, and determines the optimal vertex merging position, thereby realizing efficient mesh simplification; some people learn the connection distribution of the mesh through attention mechanism, and construct a mesh simplification model based on graph neural network.

[0006] In conclusion, the traditional hexahedral mesh simplification method does not consider the actual physical analysis result, and cannot associate the mesh structure characteristics with the analysis accuracy, thus leading to an unsatisfactory hexahedral mesh simplification effect.

[0007] Based on this, the hexahedral mesh intelligent simplification method with analysis accuracy is designed to solve the above problems. SUMMARY

[0008] The hexahedral mesh intelligent simplification method with analysis accuracy is proposed to solve the problems in the background art.

[0009] To achieve the above object, the hexahedral mesh intelligent simplification method with analysis accuracy adopts the following technical scheme:

[0010] The hexahedral mesh intelligent simplification method with analysis accuracy comprises the following steps:

[0011] Step 1: feature extraction of layers and columns of hexahedral meshes, including geometric features, topological features, quality features and physical features:

[0012] 1) defining layer / column geometric features according to geometric attributes of boundary point pairs to be merged in the layer / column deletion process;

[0013] 2) defining layer / column topological features by calculating the number of hexahedral elements contained by the layer / column and the change value of the local topological quality after the layer / column is deleted;

[0014] 3) defining layer / column quality features according to the Jacobian value and the skewness of the hexahedral element;

[0015] 4) defining layer / column physical features through the strain value of each mesh vertex;

[0016] Step 2: effectiveness check of layers and columns:

[0017] 5) avoiding the generation of poor local structures that cannot be repaired through geometric optimization by establishing geometric constraints and topological constraints;

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

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

[0020] Step 4: performing layer / column deletion operation:

[0021] 7) If the maximum deletion probability is higher than the deletion threshold, perform the deletion operation on the layer or column, and return 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, reach the simplification termination condition, and output the simplified grid.

[0022] As a further description of the above technical solution: the geometric properties of the layer / column boundary point pairs to be merged are placed in a matrix, where the geometric properties entity of each boundary grid point is pi (the i-th geometric point), cj (the j-th geometric edge), or fk (the k-th geometric face), and the layer / column geometric property 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 topology feature are as follows:

[0024] (1) Determine the number of hexahedral cells contained in the layer / column: determine the number of hexahedral cells contained in the layer / column by traversing each hexahedral cell in the layer / column;

[0025] (2) Determine the initial grid topology quality and the ideal grid topology quality: the grid topology quality can be defined based on the degree of the grid edge: where V e represents the degree of the grid edge e, i.e., the number of adjacent grid faces, VI e represents the ideal degree of the grid edge e, which is affected by its geometric properties: if the grid edge is an internal grid edge, its ideal degree should be VI e = 4; if the grid edge is located on a geometric face, its ideal degree is VI e = 3; if the 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;

[0026] (3) Determine the change value of the local topology quality after layer deletion: for layer s, the grid edges can be divided into two categories: one is the deleted grid edge, such as es, and the other is the grid edge pair to be merged, such as (ec1, ec2). The degree of the grid edge after merging the edge pair is:

[0027]

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

[0029] ​

[0030] (4) Determine the change in local topology quality after column deletion: For column c, its mesh edges can be divided into three categories: one category is mesh edge pairs parallel to the column that need to be merged, such as (eh1, eh2); another category is mesh edge pairs perpendicular to the column that need to be merged, such as (ev1, ev2); and the third category is mesh edge pairs whose adjacent structure changes, such as en1 and en2. The mesh edges after merging the mesh edge pairs parallel to the column are... The degree is:

[0031]

[0032] The grid edges perpendicular to the column are merged into a single grid edge. The degree is:

[0033]

[0034] The edge degree of the mesh where the adjacent structure changes is: Local topology quality after column deletion: Because the local topology quality of the mesh before the column was deleted was The change in mesh topology quality is

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

[0036] (1) Determine the maximum and average shear of the layer / column: For a hexahedral mesh, the face shear refers to the normalized value of the shear angle of the quadrilateral face of the parallel topology within the hexahedral cell:

[0037] Where d p1 and d p2 Let d be the perpendicular distance from the center point of two quadrilateral faces to the opposite face, and d be the distance from the center point of the quadrilateral face. The element shear is defined as the maximum value of the shear of the three faces contained in a hexahedral element, i.e., S. H =max(S) qp1 ,S qp2 ,S qp3 The maximum shear degree refers to the maximum shear degree of the corresponding volume mesh in the layer / column, that is:

[0038] S max =max{S Hi |i=1,2,...,n v The average shear rate refers to the average shear rate of the faces contained in the corresponding volume mesh in a layer / column, i.e., S. avg =avg{S Hi |i=1,2,...,n H}, wherein n H is the number of bodies;

[0039] (2) The Jacobian value is calculated by 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 layer / row physical feature extraction is: obtaining the strain value of each vertex of the layer and column, calculating the maximum strain value and the average strain value as the physical features of the layer and column, for each vertex Vsi of the layer, we assign a strain value attribute denoted as Usi, and calculate the maximum strain value and the average strain value to obtain the physical features wherein n s is the number of vertices contained in the layer, for each vertex Vci of the column, we assign a strain value attribute denoted as Uci, and calculate the maximum strain value and the average strain value to obtain the physical features wherein 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 geometric constraints and topological constraints is:

[0042] (1) Geometric constraint establishment: improper layer and column structure deletion can cause geometric invalidity of the mesh, in hexahedral mesh, geometric invalid rows can cause inaccuracy, stability problems and errors in numerical simulation, affecting analysis accuracy, therefore, it is crucial to ensure that there is no geometric invalid row 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 properties of the boundary point pair, i.e. by the geometric features of the layer / row;

[0043] (2) Topological constraint establishment: if the degree of an internal mesh edge after deleting a layer or column is less than 3, i.e. a doublet element is generated, then the layer or column cannot be deleted; if deleting a layer or column results in three vertices of a mesh face being on the same geometric edge, then the layer or column cannot be deleted.

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

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

[0046] (2) Standardize the dataset, convert the data to standard normal distribution, we calculate the mean and standard value of each feature by 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.

[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 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.

[0049] (5) Establish a neural network prediction model and test the prediction accuracy. When a low prediction accuracy is observed, we perform a repeated iteration process and go back to the first step to modify the features to continuously adjust the model until the desired prediction accuracy level is reached.

[0050] As a further description of the above technical solution: in the layer / row deletion operation, the layer deletion operation realizes the deletion of the layer structure by degrading the grid edge of the layer to a grid point, and the column deletion realizes the deletion of the column structure by merging the diagonal grid points in the grid surface of the column and degrading the grid surface to a grid edge. The maximum probability of deleting the layer / row is predicted by the trained HSimNet network, and if the maximum deletion probability is higher than the deletion threshold, the deletion operation is performed on the layer or column, and the layer and column features are updated back to step one; if all layer and column deletion probabilities are less than the deletion threshold, the simplified termination condition is reached, and the simplified grid is output.

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

[0052] 1. In the present application, layers and columns are used as the basic objects of grid simplification, and the layer and column structures are comprehensively measured from multiple dimensions of geometry, topology, quality, and physics, providing rich structural features for the construction of a grid intelligent simplification model. By introducing a machine learning algorithm, the influence of the hexahedral grid layer and column structure on the grid analysis accuracy is automatically learned from the training data, and a hexahedral grid structure intelligent simplification model is constructed, realizing the simplification of the hexahedral grid with preserved analysis accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 A flowchart of a hexahedral grid intelligent simplification method with preserved analysis accuracy is provided for the present application.

[0054] Figure 2A simplified method effect diagram of a hexahedral mesh intelligent simplification method for preserving analysis accuracy is provided in the present application, wherein Figure 2 a is a dense hexahedral mesh and analysis results; Figure 2 b is an input hexahedral mesh and analysis results, Figure 2 c is a result mesh and analysis results obtained by using the simplification method of the present application. DETAILED DESCRIPTION

[0055] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0056] Please refer to the accompanying Figure 1 - the accompanying Figure 2 The present application provides a technical solution: a structure-guided hexahedral mesh geometry optimization method, comprising the following steps:

[0057] Step 1: Feature extraction is performed on the layers and columns of the hexahedral mesh, including geometric features, topological features, quality features and physical features;

[0058] Step 2: Effectiveness check is performed on the layers and columns;

[0059] Step 3: Based on the constructed simplification neural network HSimNet, the deletion probability of the deletable layers / columns is predicted;

[0060] Step 4: Layer / column deletion operation is performed;

[0061] The main process of simplifying the hexahedral mesh by using the simplification method of the present application is shown in Figure 1 The input hexahedral mesh (with mesh vertex strain values and geometric model), feature extraction, layer / column effectiveness check, prediction of maximum layer / column deletion probability, judgment of whether the simplification condition is reached, and output of the simplified hexahedral mesh are shown in the figure.

[0062] The present application is a hexahedral mesh intelligent method for preserving analysis accuracy, which introduces neural network technology. By extracting the geometric, mesh topological, quality and physical features of the body mesh, the powerful fitting capability of the neural network is used to effectively learn the influence of the topological structure of the mesh on the analysis accuracy, so that the topological behavior with the smallest influence can be accurately predicted, and the deletion order of the layers and columns can be accurately determined. The input of the method is the hexahedral mesh and its strain analysis results, and the output is the hexahedral mesh after simplification while preserving the analysis accuracy.

[0063] In order to obtain the input feature vector of the HSimNet model, firstly, we need to extract the features of each layer and each column on the input hexahedral mesh in multiple aspects. We need to establish a feature matrix for each layer and each column.

[0064] The layer / column feature matrix is obtained in four steps: firstly, the geometric features of each layer and each column are determined according to the geometric properties of each boundary mesh vertex; secondly, the topological features of each layer and each column are determined according to the mesh topological quality; thirdly, the quality features of each layer and each column are obtained according to the skewness and Jacobian value in the mesh quality; and finally, the physical features of each layer and each column are determined according to the input strain analysis results.

[0065] With the help of the geometric model, the ACIS library can be used to obtain the geometric properties of each boundary mesh vertex, where the geometric properties of each boundary mesh point are entity, or pi (the i-th geometric point), or cj (the j-th geometric edge), or fk (the k-th geometric face). The geometric properties of each vertex in the layer / column are added 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 change value of the local topological quality after the pre-judged layer / column is deleted. The number of hexahedral elements contained in the layer / column is obtained by marking each hexahedral element and calculating the number of hexahedral elements belonging to the layer / column mark. The change value of the local topological quality after the pre-judged layer / column is deleted can be calculated by the following steps:

[0067] (1) Determine the initial mesh topological quality and the ideal mesh topological quality: The mesh topological quality can be defined based on the degree of the mesh edge: where V e represents the degree of the mesh edge e, i.e., the number of adjacent mesh faces, VI e represents the ideal degree of the mesh edge e. The ideal degree of the mesh edge 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 a geometric face, its ideal degree is VI e = 3; if the mesh 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.

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

[0069]

[0070] merged edge The ideal number of 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 grid edges can be divided into three categories, one category is the parallel grid edge pair that needs to be merged, such as (eh1, eh2), one category is the vertical grid edge pair that needs to be merged, such as (ev1, ev2), and one category is the grid edge pair whose adjacent structure changes, such as en1 and en2. The degree of the merged grid edge of the parallel grid edge pair is:

[0073]

[0074] The degree of the merged grid edge of the vertical grid edge pair is:

[0075]

[0076] The degree of the grid edge whose adjacent structure changes is: Local topological quality after column deletion: Since the local topological quality of the grid before deleting the column is The change of the grid topological quality is

[0077] Grid quality is a key factor affecting analysis accuracy. In order to ensure analysis accuracy, after determining the topological characteristics, we need to determine its quality characteristics with four dimensions: the maximum and average skewness of the hexahedral elements of the layer / column, and the minimum and average Jacobian value of the hexahedral elements of the layer / column. The quality characteristics of the layer / column can be obtained by following the steps:

[0078] (1) Determine the maximum and average skewness of the layer / column: for hexahedral grid, the face skewness refers to the normalized value of the skew angle of the four polygonal face pairs in the hexahedral element: where d p1 and d p2 are the vertical distances from the center points of the two quadrilateral faces to the opposite faces, and d is the distance between the center points of the quadrilateral face pairs. The element skewness is defined as the maximum value of the three face skewnesses contained in a hexahedral element, that is, S H = max(S qp1 , S qp2 , S qp3). The maximum skewness is the maximum skewness of the corresponding volume mesh in the layer / column, i.e., S max = max{S Hi |i = 1, 2,..., n v}. The average skewness is the average skewness of the corresponding volume mesh in the layer / column, i.e., S avg = avg{S Hi |i = 1, 2,..., n H}, where n H is the number of volumes.

[0079] (2) The Jacobian value is calculated using the method in [Zhu et al. 2014 Direct Editing on Hexahedral Mesh through Dual Operations].

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

[0081] In order to perform validity checking on the layer and column, we use its geometric features and topological structure to establish geometric constraints and topological constraints. In order to avoid the generation of geometric invalidity in the simplification process of the mesh, we determine all possible boundary point pairs that can cause geometric invalidity according to the layer / column deletion method and geometric features, as shown in Table 1. In order to avoid the generation of poor local structure that cannot be repaired by geometric optimization in the layer / column deletion process, the following topological constraints are added:

[0082] (1) If it is predicted that the deletion of a layer or column produces an internal mesh edge with a degree less than 3, i.e., a doublet element, then the layer or column cannot be deleted;

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

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

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

[0086] (2) Standardize the data set. Convert the data to standard normal distribution. We calculate the mean and standard value of each feature, and convert the data to standard normal distribution by 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.

[0087] (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.

[0088] (4) Select the optimizer, loss function, and activation function. Use the stochastic gradient descent optimizer (SGD), and select the mean square error (MSE) as the loss function. Select relu as the activation function.

[0089] (5) Establish the neural network prediction model, and test the prediction accuracy. When a lower prediction accuracy is observed, we perform a repeated iteration process, and go back to the first step to modify the features, in order to continuously adjust the model until the desired prediction accuracy level is reached.

[0090] For the removable layers / rows predicted by the pre-judgment, according to their topology, quality, and physical characteristics, use HSimNet to calculate the deletion probability.

[0091] The layer deletion method in step 4) adopts [Borden MJ et al 2002 Coarsening and sheet extraction for all-hexahedral meshes.]. Column deletion is achieved by merging diagonal mesh points in the mesh face of the column, degenerating the mesh face into mesh edges, thus deleting the column structure. All deletable layers / columns are traversed, and the layer i with the highest deletion probability is determined. The deletion operation is performed on this layer, and the local mesh is optimized using a local Laplace geometry optimization method. The features of the affected layers / columns are updated in the simplified mesh, and the mesh simplification is iteratively repeated according to the above steps until the termination condition is met. In the feature update stage of the simplified mesh, only the features of layers / columns adjacent to or intersecting with the deleted layer / column are updated. Geometric, topological, and quality features are recalculated, while the strain value of the newly generated mesh vertex v' is the average strain value of the two original mesh vertices merged into that vertex. Where u' is the strain value of the newly generated mesh vertex, u i and u j These are the two vertices merged into v' during layer / column deletion. Mesh simplification terminates when the simplified mesh meets one of the following two conditions: 1) All layers and columns of the simplified mesh are non-deletable; 2) The probability of deleting all deletable layers and columns of the simplified mesh is less than 96%.

[0092] For the simplified mesh, linear interpolation is used to solve for the true solution of each vertex. For each mesh vertex v, first determine which hexahedral cell in mesh H the vertex is located in, and then use barycentric coordinate interpolation to obtain the true solution of vertex v based on the true solution of the vertex of that hexahedral cell. For each vertex v of the mesh before and after simplification... i The relative error of the displacement value is Where u i For grid vertex v i The actual strain displacement value, This represents the actual displacement value of the grid point.

[0093] like Figure 2 As shown, a comparison diagram of the simplified hexahedral mesh results obtained using the simplification method proposed in this invention is presented. Figure 2 a represents a dense hexahedral mesh and the analysis results; Figure 2 b represents the input hexahedral mesh and analysis results, with a minimum Jacobian value of 0.73, an average Jacobian value of 1.0, a maximum relative error of 3.07%, and an average relative error of 0.45%. Figure 2 c represents the resulting mesh and analysis results using the simplified method of this invention. The lowest Jacobian value is 0.28, the average Jacobian value is 0.86, the maximum relative error is 2.05%, and the average relative error is 0.82%. Figure 2As can be seen from the simplification effect, the simplification method of the application can not only significantly reduce the number of grid units, but also maintain the analysis accuracy of the model as a whole, and realize the precision-keeping hexahedral mesh simplification.

[0094] The above merely describes the preferred embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can make equivalent replacements or changes to the technical solutions and the inventive concept of the present application within the technical range disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for intelligent simplification of hexahedral meshes while maintaining analytical accuracy, characterized in that, Includes the following steps: 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 geometric features of the layer / column based on the geometric attributes of the boundary point pairs to be merged during the layer / column deletion process; 2) Define the topological features of a layer / column by calculating the number of hexahedral elements 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 rate of the hexahedral elements; 4) Define the physical characteristics of the layer / column using the strain value of each mesh vertex; Step 2: Perform validity checks on layers and columns: 5) By establishing geometric and topological constraints, poor local structures that cannot be repaired through geometric optimization are avoided; Step 3: Based on the constructed simplified neural network HSimNet, predict the deletion probability of deletable layers / columns: 6) Construct the HSimNet network architecture using neural networks and predict the deletion probability of removable layers / columns; The process of constructing the HSimNet network architecture: (1) Based on the selected features, we construct the dataset. We randomly divide the training set and the validation set into two sets with a ratio of 80% and 20%. After obtaining the training set, we extract the feature information from it and generate training files according to the order of the features. The training files are used for sample learning. (2) Standardize the dataset by converting the data into a standard normal distribution. We do this by calculating the mean and standard value of each feature. Where Z is the standardized value and X is the original value. It is the mean of the original values. It is the standard deviation of the original values; (3) Select appropriate hyperparameters, such as 8 input layers, 30 first hidden layers, 12 second hidden layers, and a learning rate of 0.001; (4) Select the optimizer, loss function, and activation function. Use the stochastic gradient descent optimizer (SGD), and select mean squared error (MSE) as the loss function and 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, returning to the first step to modify the features, so as to continuously adjust the model until the desired prediction accuracy level was achieved. Step 4: Perform layer / column deletion operation: 7) If the maximum deletion probability is higher than the deletion threshold, perform the deletion operation on the layer or column and return to step one to update the layer and column features; if the deletion probability of all layers and columns is 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 while maintaining analytical accuracy according to claim 1, characterized in that, In the aforementioned layer / column geometric features, the geometric attributes of the boundary point pairs that need 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 the layer / column geometric attribute matrix is ​​constructed as the geometric features of the layer / column.

3. The intelligent simplification method for hexahedral meshes while maintaining analytical accuracy according to claim 1, characterized in that, The specific steps for defining layer / column topological features by calculating the number of hexahedral cells contained in the layer / column and the predicted change in local topological quality after layer / column deletion are as follows: (1) Determine the number of hexahedral units contained in a layer / column: By traversing the hexahedrons of each layer / column, determine the number of hexahedrons contained in that layer / column; (2) Determine the initial mesh topology quality and the ideal mesh topology quality: Mesh topology quality can be defined based on the degree of the mesh edges. ,in Represents grid edges The degree, that is, the number of adjacent grid faces. Represents grid edges The ideal degree of a mesh edge is influenced by its geometric properties: if the mesh edge is an internal mesh edge, its ideal degree should be... =4; if the grid edge lies on a geometric surface, then its ideal degree is =3; If the grid edge lies on a geometric edge, its ideal degree should be determined based on the dihedral angle of the geometric edge. ,in The angle measures of the two sides 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 merging 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 topology quality after column deletion: For column c, its mesh edges can be divided into three categories: one category is mesh edge pairs parallel to the column that need to be merged, such as (eh1, eh2); another category is mesh edge pairs perpendicular to the column that need to be merged, such as (ev1, ev2); and the third category is mesh edge pairs whose adjacent structure changes, such as en1 and en2. The mesh edges after merging the mesh edge pairs parallel to the column are... The degree is: ； The grid edges perpendicular to the column are merged into a single grid edge. The degree is: ； The edge degree of the mesh whose adjacent structure changes is: Local topology quality after column deletion: Because the local topology quality of the mesh before the column was deleted was The change in mesh topology quality is .

4. The intelligent simplification method for hexahedral meshes while maintaining analytical accuracy according to claim 1, characterized in that, The process of extracting the layer / column quality features is as follows: (1) Determine the maximum and average shear rate of the layer / column: For a hexahedral mesh, the face shear rate refers to the normalized value of the shear angle of the quadrilateral face of the parallel topology within the hexahedral cell: ,in and Let d be the perpendicular distance from the center point of two quadrilateral faces to the opposite face, and d be the distance from the center point of the quadrilateral face. The element shear is defined as the maximum value of the shear of the three faces contained in a hexahedral element, i.e. Maximum shear refers to the maximum shear value of the corresponding volume mesh in the layer / column, i.e.: The average shear rate refers to the average shear rate of the faces contained in the corresponding volume mesh in a layer / column, i.e. ,in The number of bodies; (2) The Jacobian value was calculated using the method described in [Zhu et al. 2014 Direct Editing on Hexahedral Meshthrough Dual Operations].

5. The intelligent simplification method for hexahedral meshes while maintaining analytical accuracy according to claim 1, characterized in that, The process of establishing the geometric and topological constraints is as follows: (1) Establishing geometric constraints: Inappropriate deletion of layer and column structures can lead to geometric invalidity of the mesh. In a hexahedral mesh, geometrically invalid rows may cause inaccuracies, instability 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 in order to guarantee the accuracy and reliability of the simulation and avoid potential consequences. This invalidity can be determined by the geometric properties of the boundary point pairs, that is, by the geometric characteristics of the layers / columns. (2) Establishment of topological constraints: If the deletion of a certain layer or column produces an internal mesh edge with a degree less than 3, i.e., a doublet element, then the layer or column cannot be deleted; if the deletion of a certain layer or column results in the three vertices of a certain mesh surface being on the same geometric edge, then the layer or column cannot be deleted.

6. The intelligent simplification method for hexahedral meshes while maintaining analytical accuracy according to claim 1, characterized in that, In the layer / column deletion operation, the layer deletion operation removes the layer structure by degenerating the grid edges of the layer into grid points, and the column deletion removes the column structure by merging the diagonal grid points in the grid face of the column and degenerating the grid face into grid edges. Through the trained HSimNet network, the layer / column with the highest probability of deletion is predicted and deleted. If the highest deletion probability is higher than the deletion threshold, the layer or column is deleted and the process returns to step one to update the layer and column features. If the deletion probability of all layers and columns is less than the deletion threshold, the simplification termination condition is reached, and the simplified grid is output.

Images