Mesh quality evaluation method for electromagnetic simulation software based on neural network

Abstract

A neural network-based method for evaluating the mesh quality of electromagnetic simulation software solves the problems of existing methods, such as long model training time, long data generation time, and the need for manual judgment of mesh surface quality. The implementation steps of the method are as follows: generating a finite element mesh data file; generating a far-field radar cross-section root mean square error data set; generating a training sample set; constructing a mesh quality evaluation model; training the mesh quality evaluation model; and evaluating the mesh quality. The present invention uses Latin hypercube sampling to select data, and the normalized mesh features and the normalized far-field radar cross-section root mean square error form a training set, and constructs and trains a mesh quality evaluation model composed of multiple linear layers cascaded. The present invention improves the efficiency of mesh quality evaluation and has the advantages of low cost, objectivity, and unified evaluation standards.

Description

Technical Field

[0001] The present invention belongs to the field of physics technology and further relates to a neural network-based mesh quality evaluation method for electromagnetic simulation software in the finite element method. The present invention can be used to evaluate the quality of meshes generated by the finite element method of electromagnetic simulation software using scatterers. Background Art

[0002] With the rapid development and popularization of computer technology, the finite element method has rapidly expanded from engineering structure strength analysis to almost all scientific and technological fields, becoming a widely used and efficient numerical analysis method. Early finite element analysis research focused on deriving new high-efficiency solution methods and high-precision units. With the gradual improvement of numerical analysis methods and the rapid increase in computer computing speed, the time required for the entire computing system to solve calculations has become increasingly shorter, while problems with data preparation and the performance of calculation results have become increasingly prominent. Meshing, as an important step in establishing finite element models, requires many considerations and a large amount of work. Different meshing methods can have a significant impact on the calculation scale, calculation results, and calculation accuracy of the finite element model. Therefore, research on finite element mesh quality is very important.

[0003] The Computational Aerodynamics Research Institute of the China Aerodynamics Research and Development Center has disclosed a mesh surface quality detection method based on deep learning in its published patent document "A mesh surface quality detection method based on deep learning" (application number: CN:202011205869:A, application publication number: CN112307673A). This method mainly solves the problem of mesh surface quality detection. The implementation steps of this method are: (1) constructing a mesh surface dataset and dividing the established mesh surface dataset into a training dataset and a test dataset; (2) marking the training data and marking the quality of the mesh surface; (3) constructing a mesh surface quality detection network and performing detection to obtain a trained mesh surface quality detection network; (4) judging the quality of the mesh surface and outputting the quality judgment of the mesh surface. Although this method realizes automatic, efficient and accurate multi-level feature extraction, it overcomes the shortcomings of relying on complex manual operations to judge mesh quality in the past. However, this method still has three shortcomings. First, in the process of constructing the grid surface dataset, this method directly converts the three-dimensional grid data into two-dimensional grid data to construct the dataset. The grid surface has many data features, which leads to a high number of input nodes and a long time consumption during model training, which further leads to the low efficiency of the grid quality evaluation of this method. Second, in the process of constructing the grid surface dataset, this method requires a large amount of data to construct the training set. The data generation process consumes a long time, which leads to the low efficiency of the grid quality evaluation of this method. Third, in the process of marking the quality of the grid surface, this method still needs to manually judge the quality of the grid surface, which leads to high cost, high subjective component, and inconsistent evaluation standards. Summary of the Invention

[0004] The purpose of the present invention is to address the problems existing in the above-mentioned prior art and propose a neural network-based grid quality evaluation method for electromagnetic simulation software to solve the problems of low grid quality evaluation efficiency and heavy reliance on manual judgment of the final results in existing grid quality evaluation tasks.

[0005] The idea of ​​achieving the purpose of the present invention is as follows: the present invention analyzes the grid data features that affect the simulation results found in the design process of electromagnetic simulation software, and then directly extracts grid feature variable data from the three-dimensional finite element grid data. Compared with directly converting the three-dimensional grid data into two-dimensional grid data to construct a data set, the length of the grid data and the number of input layer nodes when training the model are simplified, the time consumption in the training model process is reduced, and the efficiency of grid quality evaluation is improved. The present invention uses the Latin hypercube sampling method to select data for grid division, which improves the uniformity of data distribution. Compared with generating data using random methods, it reduces the amount of data required, saves the time consumed in the data generation process, and improves the efficiency of grid quality evaluation. The present invention uses the far-field radar cross-section simulation data obtained by electromagnetic simulation software to calculate the root mean square error of the far-field radar cross-section to judge the quality of the grid surface. Compared with manual judgment of grid quality, the cost is lower, the evaluation is more objective, and the evaluation standard is more unified.

[0006] The specific steps for achieving the purpose of the present invention are as follows:

[0007] Step 1: Generate finite element mesh data file:

[0008] Step 1.1, construct a three-dimensional model of the scatterer using engineering numerical simulation software;

[0009] Step 1.2, using the Latin hypercube sampling method, select A data in each set value interval to form a data group, where A ≥ 100, and each set value interval is a value interval selected for each setting parameter according to the interval requirement of the parameter setting in the engineering numerical simulation software;

[0010] Step 1.3: Import the data in the data set into the engineering numerical simulation software in B batches, replace the parameter values ​​set in the engineering numerical simulation software with the data imported each time, mesh the scatterer three-dimensional model, and output the meshing result to obtain a finite element mesh data file, where the value of B is equal to the value of A.

[0011] Step 2: Generate the far-field radar cross-section root mean square error dataset:

[0012] Step 2.1: Use the target electromagnetic simulation software to construct a three-dimensional model of the scatterer. Import each finite element mesh data file into the target electromagnetic simulation software in sequence, replace the mesh generation result of the target electromagnetic simulation software with the finite element mesh data file imported each time, simulate the three-dimensional scatterer model, and obtain a set of far-field radar cross-section data corresponding to the simulation. The far-field radar cross-section data corresponding to all simulations are combined into a far-field radar cross-section data set.

[0013] Step 2.2: Use comparative electromagnetic simulation software to construct a three-dimensional model of the scatterer, automatically generate a meshing result using the comparative electromagnetic simulation software, simulate the three-dimensional scatterer model based on the meshing result, and obtain a set of far-field radar cross-section simulation data corresponding to the meshing result;

[0014] Step 2.3, calculating the root mean square error between each set of far-field radar cross section data in the far-field radar cross section data set and the far-field radar cross section simulation data, forming all the far-field radar cross section root mean square error data into a far-field radar cross section root mean square error data set and normalizing them;

[0015] Step 3: Generate training set:

[0016] Step 3.1, extracting no less than 10 mesh data from each finite element mesh data file according to the feature extraction standard;

[0017] Step 3.2: assemble the mesh data extracted from all mesh finite element mesh data files into a mesh feature set, and normalize the mesh feature set;

[0018] Step 3.3, the normalized grid feature set and the normalized far-field radar cross section root mean square error data set are combined into a training set;

[0019] Step 4: Build a mesh quality evaluation model:

[0020] A mesh quality evaluation model consisting of seven linear layers with the same structure was built. The number of nodes in the first to seventh linear layers of the model was set to 14, 32, 64, 32, 16, 8, and 1, respectively. The node random deactivation rate was set to 0.3, 0.4, 0.2, 0.3, 0.1, 0.2, and 0, respectively.

[0021] Step 5: Train the grid quality evaluation model:

[0022] Step 5.1, set the training parameters, where the initial learning rate is set to 0.01, the batch size is set to 32, and the momentum of the gradient descent method is set to 0.9;

[0023] In step 5.2, the training set is input into the mesh quality assessment model, and the gradient descent method is used to iteratively update the network parameters until the loss function converges, thereby obtaining a trained mesh quality assessment model.

[0024] Step 6: Evaluate the mesh quality:

[0025] Step 6.1, using the same method as steps 3.1 and 3.2, the finite element mesh data file to be evaluated is processed to obtain normalized mesh features;

[0026] In step 6.2, the normalized mesh features are input into the trained mesh quality evaluation model, and the mesh quality prediction score corresponding to the mesh data file to be evaluated is output.

[0027] Compared with the prior art, the present invention has the following advantages:

[0028] First, because the present invention extracts grid features from three-dimensional grid data, it overcomes the shortcomings of the prior art of directly converting three-dimensional grid data into two-dimensional grid data to construct a data set, resulting in low grid quality evaluation efficiency due to the large number of data features during model training, the large number of model training input layer nodes, and the long model training time. The present invention simplifies the dimension of each group of grid data and the dimension of the data when training the model, reduces the time consumed by model training, and has the advantage of higher grid quality evaluation efficiency.

[0029] Second, because the present invention uses the Latin hypercube sampling method to select data for grid division, it overcomes the shortcomings of the existing technology that the grid quality evaluation efficiency is low due to the need to generate a large amount of random data and the large amount of time consumed in data generation. The present invention improves the uniformity of data distribution, reduces the data demand, saves the time consumed in generating data, and has the advantage of higher grid quality evaluation efficiency.

[0030] Third, since the present invention uses the far-field radar cross-section simulation data obtained through electromagnetic simulation software to calculate the root mean square error of the far-field radar cross-section to evaluate the quality of the grid surface, it overcomes the shortcomings of the existing technology of high cost, high subjective component, and inconsistent evaluation standards due to the need to manually judge the quality of the grid surface. The present invention eliminates the impact of manual evaluation and has the advantages of low cost, objectivity, and unified evaluation standards. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is an implementation flow chart of the present invention. DETAILED DESCRIPTION

[0032] The following is combined with Figure 1 The present invention is further described with simulation experiments.

[0033] Step 1: Generate finite element mesh data file.

[0034] In step 1.1, using the Latin hypercube sampling method, 160 data points are selected in the intervals [0, 1] and [0.01, 0.05] to form a two-dimensional data set. The intervals [0, 1] and [0.01, 0.05] are chosen because the engineering numerical simulation software GiD (GiD Professional) has two setting parameters: the mesh size value and the mesh transition factor. These two setting parameters must be within the intervals [0, 1] and [0.01, 0.05], respectively. If these values ​​exceed this interval, GiD will not be able to perform effective meshing.

[0035] In step 1.2, in an embodiment of the present invention, GiD is used to construct an Ogive 3D model. The data from the 2D data set is imported into the GiD software 160 times. The two imported data are used to replace the values ​​of the two setting parameters in the GiD software, namely the mesh size and mesh transition factor. The mesh size and mesh transition factor values ​​in the GiD software are updated 160 times in total. Each time, the GiD software performs meshing based on the mesh size and mesh transition factor, obtaining the meshing result. The GiD software outputs each meshing result as a finite element mesh data file corresponding to the meshing result, ultimately obtaining 160 different finite element mesh data files.

[0036] Step 2: Generate a far-field radar cross-section root mean square error dataset.

[0037] In step 2.1, construct an Ogive 3D model using the target electromagnetic simulation software. Import the finite element mesh data file into the target electromagnetic simulation software 160 times, replacing the target electromagnetic simulation software's mesh generation results with the imported finite element mesh data file each time. Update the target electromagnetic simulation software's mesh generation results 160 times in total. Simulate the Ogive 3D model based on the mesh generation results each time, obtaining a set of far-field radar cross-section data for 180 angles within the angular domain centered at the center of the Ogive 3D model corresponding to that simulation. The resulting 160 sets of far-field radar cross-section data constitute the far-field radar cross-section dataset.

[0038] In step 2.2, a 3D model of the Ogive is constructed using the electromagnetic simulation software HFSS (High Frequency Structure Simulator). HFSS automatically generates a meshing result. The Ogive 3D model is simulated based on this meshing result, generating a set of far-field radar cross-section simulation data for 180 angles within the angular domain centered at the Ogive center.

[0039] Step 2.3: Calculate the RMS error (RMS) between each set of far-field RCS data in the far-field RCS dataset and the simulated far-field RCS data, obtaining a set of RMS Estimation data corresponding to that far-field RCS data. Calculate the RMS error 160 times in total. The resulting 160 sets of RMS Estimation data constitute the far-field RCS RMS Estimation dataset, and normalize the far-field RCS RMS Estimation dataset.

[0040] Step 3: Generate a training set.

[0041] In step 3.1, according to the feature extraction criteria (see Table 1), 7 features were selected from each finite element mesh data file, with 2 values ​​for each feature extracted, resulting in a total of 14 mesh data. These 14 mesh data were then combined into a mesh feature set corresponding to the finite element mesh data file. The resulting 160 different mesh features were then normalized to obtain a normalized mesh feature set.

[0042] Table 1. Features and extraction criteria

[0043]

[0044] In step 3.2, the normalized grid feature set and the normalized far-field radar cross-section root mean square error data set are combined into a sample set.

[0045] Step 4: Construct a grid quality evaluation model.

[0046] A mesh quality assessment model consisting of seven cascaded linear layers with the same structure was constructed. In this embodiment of the present invention, the number of nodes in the first to seventh linear layers of the model was set to 14, 32, 64, 32, 16, 8, and 1, respectively; and the node random deactivation rate was set to 0.3, 0.4, 0.2, 0.3, 0.1, 0.2, and 0, respectively.

[0047] Step 5: Train the grid quality evaluation model.

[0048] Step 5.1, set training parameters. In this embodiment, the training parameters are set as follows: the initial learning rate is set to 0.01, the batch size is set to 32, and the momentum of the gradient descent method is set to 0.9.

[0049] In step 5.2, the training set is input into the grid quality evaluation model, and the network parameters are iteratively updated using the gradient descent method until the loss function converges to obtain a trained grid quality evaluation model.

[0050] Step 6: Evaluate the mesh quality.

[0051] Step 6.1: Use the target electromagnetic simulation software to construct an Ogive three-dimensional model and mesh the three-dimensional model. The meshing result output by the simulation software is used as the finite element mesh data file to be evaluated.

[0052] In step 6.2, the same method as in step 3.1 is used to extract features and normalize the finite element mesh data file to be evaluated in sequence to obtain normalized mesh features.

[0053] In step 6.3, the normalized mesh features are input into the trained mesh quality evaluation model, and the mesh quality prediction score corresponding to the mesh feature data is output.

[0054] The effects of the present invention will be further described below with reference to specific embodiments:

[0055] 1. Simulation experiment conditions:

[0056] The hardware platform of the simulation experiment of the present invention is: the processor is Intel (R) Xeon (R) CPU E3-1230 v3 @ 3.30GHz, the main frequency is 3.30GHz, the memory is 24GB, and the graphics card is NVIDIA GeForce GT 630.

[0057] The software platform for the simulation experiment of the present invention is: Windows Professional Edition 21H1 operating system, PyTorch-gpu1.9.0 open source deep learning framework, and Python 3.8.

[0058] The scatterers used in the simulation experiment of the present invention are Ogive head, Ogive tail, Double Ogive head, and Double Ogive tail, respectively. The material is aluminum, and the calculation frequency is 7 GHz.

[0059] 2. Simulation content and results analysis

[0060] The simulation experiment of the present invention adopts the present invention and the existing technology (grid surface quality detection method), respectively using target electromagnetic simulation software to segment the three-dimensional models of four scatterers, and performing quality evaluation on the grid segmentation results output by the software to obtain the grid quality evaluation results of the four scatterers.

[0061] The four scatterers refer to the Ogive head, Ogive tail, Double ogive head, and Double ogive tail respectively.

[0062] The mesh surface quality detection method in the prior art refers to the mesh surface quality evaluation method based on deep learning mentioned in the published patent document "A mesh surface quality detection method based on deep learning" (application number: CN:202011205869:A, application publication number: CN112307673A) of the Institute of Computational Aerodynamics, China Aerodynamics Research and Development Center.

[0063] To evaluate the mesh quality evaluation results of the present invention and the prior art, four evaluation metrics (number of training samples, number of input layer nodes, need for manual judgment, and accuracy) were used to evaluate the quality evaluation results of the two simulation methods. The accuracy of the mesh quality evaluation results of the four scatterers was calculated using the following formula, and all the results are plotted in Table 2:

[0064]

[0065] Table 2. Analysis of mesh quality evaluation results of the present invention and prior art in simulation experiments

[0066]

[0067] As can be seen from Table 1, the accuracy of the mesh quality evaluation results of the present invention for four scatterers is 97%, 97%, 97%, and 94%, respectively. The number of required training samples is 160, and the number of input layer nodes is 14. The accuracy is higher than that of existing methods, while the number of training samples and input layer nodes is far lower than that of existing methods. At the same time, the present invention completely eliminates the need for manual judgment of mesh surface quality. This proves that the present invention can improve the efficiency of mesh quality evaluation while maintaining accuracy, and obtain low-cost, objective evaluation results with unified evaluation standards.

[0068] The above simulation experiments show that: the method of the present invention utilizes the method of extracting grid feature variables to streamline the number of nodes in the input layer during model training, reduces the time consumed by model training, and solves the shortcomings of low grid quality evaluation efficiency caused by many data features, many nodes in the model training input layer, and long model training time in the prior art; the Latin hypercube sampling method is used to generate grid subdivision features, and then the grid subdivision features are used to generate three-dimensional finite element grid data, which can improve the uniformity of data distribution, reduce data requirements, save time consumed in generating data, and solve the shortcomings of low grid quality evaluation efficiency caused by the need to generate a large amount of random data and a large amount of time consumed in data generation in the prior art; the root mean square error of the far-field radar scattering cross section of two electromagnetic simulation software is used to judge the quality of the grid surface, eliminating the influence of manual evaluation, and solving the shortcomings of high cost, high subjective component, and inconsistent evaluation standards caused by the need to manually judge the quality of the grid surface in the prior art. It is a very practical grid quality evaluation method.

Claims

1. A neural network-based method for evaluating the mesh quality of electromagnetic simulation software, characterized in that: The Latin hypercube sampling method was used to select data. The normalized mesh features and the normalized root mean square error of the far-field radar cross section were used to form a training set. A mesh quality evaluation model consisting of multiple linear layers was constructed. The specific steps of this evaluation method include the following: Step 1: Generate finite element mesh data file: Step 1.1, construct a three-dimensional model of the scatterer using engineering numerical simulation software; Step 1.2, using the Latin hypercube sampling method, select A data in each set value interval to form a data group, where A ≥ 100, and each set value interval is a value interval selected for each setting parameter according to the interval requirement of the parameter setting in the engineering numerical simulation software; Step 1.3: Import the data in the data set into the engineering numerical simulation software in B batches, replace the parameter values ​​set in the engineering numerical simulation software with the data imported each time, mesh the scatterer three-dimensional model, and output the meshing result to obtain a finite element mesh data file, where the value of B is equal to the value of A. Step 2: Generate the far-field radar cross-section root mean square error dataset: Step 2.1: Use the target electromagnetic simulation software to construct a three-dimensional model of the scatterer. Import each finite element mesh data file into the target electromagnetic simulation software in sequence, replace the mesh generation result of the target electromagnetic simulation software with the finite element mesh data file imported each time, simulate the three-dimensional scatterer model, and obtain a set of far-field radar cross-section data corresponding to the simulation. The far-field radar cross-section data corresponding to all simulations are combined into a far-field radar cross-section data set. Step 2.2: Use comparative electromagnetic simulation software to construct a three-dimensional model of the scatterer, automatically generate a meshing result using the comparative electromagnetic simulation software, simulate the three-dimensional scatterer model based on the meshing result, and obtain a set of far-field radar cross-section simulation data corresponding to the meshing result; Step 2.3, calculating the root mean square error between each set of far-field radar cross section data in the far-field radar cross section data set and the far-field radar cross section simulation data, forming all the far-field radar cross section root mean square error data into a far-field radar cross section root mean square error data set and normalizing them; Step 3: Generate training set: Step 3.1, extracting no less than 10 mesh data from each finite element mesh data file according to the feature extraction standard; Step 3.2: assemble the mesh data extracted from all mesh finite element mesh data files into a mesh feature set, and normalize the mesh feature set; Step 3.3, the normalized grid feature set and the normalized far-field radar cross section root mean square error data set are combined into a training set; Step 4: Build a mesh quality evaluation model: A mesh quality evaluation model consisting of seven linear layers with the same structure was built. The number of nodes in the first to seventh linear layers of the model was set to 14, 32, 64, 32, 16, 8, and 1, respectively. The node random deactivation rate was set to 0.3, 0.4, 0.2, 0.3, 0.1, 0.2, and 0, respectively. Step 5: Train the grid quality evaluation model: Step 5.1, set the training parameters, where the initial learning rate is set to 0.01, the batch size is set to 32, and the momentum of the gradient descent method is set to 0.9; In step 5.2, the training set is input into the mesh quality assessment model, and the gradient descent method is used to iteratively update the network parameters until the loss function converges, thereby obtaining a trained mesh quality assessment model. Step 6: Evaluate the mesh quality: Step 6.1, using the same method as steps 3.1 and 3.2, the finite element mesh data file to be evaluated is processed to obtain normalized mesh features; In step 6.2, the normalized mesh features are input into the trained mesh quality evaluation model, and the mesh quality prediction score corresponding to the mesh data file to be evaluated is output.

2. The neural network-based electromagnetic simulation software grid quality evaluation method according to claim 1, characterized in that: The root mean square error between each set of far-field radar cross section data in the far-field radar cross section data set calculated in step 2.3 and the far-field radar cross section simulation data is obtained by the following formula: Where MSE represents the root mean square error between the far-field radar cross section data and the far-field radar cross section simulation data, D represents the total number of data in the far-field radar cross section data, represents the dth radar cross section data in the far-field radar cross section data, Represents the dth radar cross section simulation data in the far-field radar cross section simulation data.

3. The neural network-based electromagnetic simulation software grid quality evaluation method according to claim 1, characterized in that: The feature extraction criteria described in step 3.1 refer to the finite element mesh features whose correlation with the far-field radar cross-section root mean square error data is greater than 0.3, obtained by performing parameter correlation analysis on the finite element mesh data and the far-field radar cross-section root mean square error data.

4. The neural network-based electromagnetic simulation software grid quality evaluation method according to claim 1, characterized in that: The loss function described in step 5.2 is as follows: Where L(·) represents the loss function of the grid quality assessment model, represents the normalized radar cross section data of the i-th batch in the training set, y i It represents the grid evaluation prediction value output by the grid quality evaluation model for the i-th batch of data in the training set, n represents the total number of samples in the training set, the value of n is equal to the value of A, ∑ represents the summation operation, i represents the data sequence number in the training set, and |·| represents the absolute value operation.

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