Method for predicting grid quality of electromagnetic calculation model based on deep belief network

Abstract

The invention discloses a method for predicting the grid quality of an electromagnetic calculation model based on a deep belief network, and belongs to the technical field of computational electromagnetism. The method comprises the following steps: S1, establishing a grid model sample library; s2, calculating a grid quality evaluation index of each subdivision model; s3, calculating an error between an electromagnetic numerical calculation result and a reference result; s4, constructing a deep belief network data set based on the steps S2 and S3; s5, constructing a deep belief network structure; and S6, calculating a grid quality evaluation index of the to-be-estimated subdivision model, taking the grid quality evaluation index as input data of the deep belief network model, and outputting to obtain prediction precision of the to-be-estimated subdivision model. The problems that in the prior art, evaluation of the influence of grid quality on the accuracy of an electromagnetic numerical algorithm depends on manpower, and the evaluation efficiency is low are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of computational electromagnetics, and in particular to a method for predicting the grid quality of an electromagnetic calculation model based on a deep belief network. Background Art

[0002] In the field of computational electromagnetics, the quality of the grid has a great impact on electromagnetic numerical algorithms.

[0003] One is the accuracy impact. The grid quality directly affects the calculation accuracy of electromagnetic numerical algorithms. High-quality grids can provide a more accurate geometric representation, thereby improving the accuracy of the algorithms. On the contrary, low-quality grids usually introduce a large number of distortions and irregular shapes, which will affect the numerical stability of electromagnetic numerical algorithms, thereby reducing the calculation accuracy of the algorithms. For example, in the method of moments, low-quality grids may lead to the generation of ill-conditioned matrices, making the numerical solution unstable.

[0004] Two is the convergence impact. The grid quality also affects the convergence of the algorithms. High-quality grids can better match the geometric structure and usually converge to the accurate solution faster, while low-quality grids may require more iterations to reach the same accuracy, affecting the convergence speed of numerical algorithms.

[0005] Three is the calculation efficiency impact. The grid quality also affects the calculation efficiency of the algorithms. High-quality grids can usually calculate results faster, while low-quality grids may require more computing resources to obtain the same results.

[0006] Four is the numerical error. Low-quality grids may introduce more numerical errors, especially in regions with sharp geometric features or high gradients. These errors may accumulate in the results of electromagnetic numerical algorithms and affect the final calculation accuracy.

[0007] Grids with high quality correspond to high simulation accuracy and accurate predicted electromagnetic performance results; grids with low quality correspond to large errors in simulation results and large deviations in predicted electromagnetic performance results. Therefore, it is of great significance to evaluate the impact of grid quality on electromagnetic numerical algorithms. In the traditional way, considering the impact of grid quality on electromagnetic numerical algorithms usually involves manually comparing the simulation results with reference data and performing data post-processing on the meshed grid model, which is not only time-consuming and laborious but also occupies a large amount of computing resources, and the meshing is highly dependent on user experience. Summary of the Invention

[0008] Aiming at the deficiencies of the existing technology, the present invention provides a method for predicting the grid quality of an electromagnetic calculation model based on a deep belief network. The method of the present invention can predict the degree of influence of grid quality on the accuracy of electromagnetic numerical algorithms, so as to be able to select appropriate grid density and other indicators to improve the accuracy of electromagnetic numerical calculations.

[0009] The technical solution adopted by the present invention is as follows:

[0010] A method for predicting the grid quality of an electromagnetic calculation model based on a deep belief network, comprising the following steps:

[0011] S1. Randomly divide a given plurality of object models to establish a grid model sample library;

[0012] For a given plurality of object models, randomly divide the surfaces of each object model within a preset grid density range; extract the grid division node coordinates of different object models under different grid densities and different triangular grid element geometric indexes, and construct a grid model sample library.

[0013] S2. Calculate the grid quality evaluation indexes of each divided model;

[0014] Select 4 parameters affecting the grid quality as grid quality evaluation indexes;

[0015] The 4 selected parameters are: element side length, element interior angle, element quality parameter, and element twist angle.

[0016] S3. Calculate the error between the electromagnetic numerical calculation result and the reference result;

[0017] Adopt the selected electromagnetic numerical algorithm to calculate each divided model in the grid model sample library to obtain the electromagnetic numerical calculation results of all divided models;

[0018] Use a commercial electromagnetic simulation software to calculate a given plurality of object models to obtain the reference results of each object model;

[0019] Compare and calculate the electromagnetic numerical calculation results of each divided model with the corresponding reference results to obtain the root mean square error.

[0020] S4. Construct a deep belief network data set;

[0021] Use the grid quality evaluation indexes of all divided models as inputs and the root mean square error corresponding to the divided models as labels to construct a deep belief network data set.

[0022] S5. Construct a deep belief network structure;

[0023] Determine the deep belief network structure, including the number of nodes and the number of layers; the number of nodes and the number of layers are determined by the following formula:

[0024]

[0025] Among them, α is an arbitrary value variable that can be taken, and can take any integer between 1 and 10, N his the number of neuron nodes in the hidden layer of the deep belief network structure, N i is the number of neuron nodes in the input layer of the hidden layer of the deep belief network structure, N o is the number of neuron nodes in the output layer of the hidden layer of the deep belief network structure.

[0026] Use the deep belief network dataset to test and verify the constructed deep belief network structure, and obtain a trained deep belief network model.

[0027] Furthermore, during the training process, set the network parameters of the deep belief network structure, including the maximum number of iterations, learning rate, activation function, and loss function. The activation function S(x) and the loss function f(x) are respectively:

[0028]

[0029] f(x) = max(0, x)

[0030] where x represents the independent variable of the function; the activation function is used to introduce non-linearity, control the output range and gradient propagation, and enhance the generalization ability of the model; the loss function is used to quantify the model prediction error and guide the parameter optimization direction.

[0031] S6. Perform mesh dissection on the object model to be electromagnetically calculated to obtain an estimated dissection model; calculate the mesh quality evaluation index of the estimated dissection model as the input data of the deep belief network model, and output the prediction accuracy of the estimated dissection model.

[0032] Furthermore, the calculation formula for the unit side length is:

[0033] edge = |v1| 2 + |v2| 2

[0034] where v1 and v2 respectively represent two vectors starting from the same node within a triangular mesh unit.

[0035] The calculation formula for the unit interior angle is:

[0036]

[0037] The unit quality parameter is:

[0038]

[0039] where v1, v2, and v3 respectively represent three vectors within a triangular mesh unit.

[0040] The calculation formula for the unit twist angle is:

[0041] θskew = 90° - min(α1, α2, α3)

[0042] Wherein, α1, α2, and α3 respectively represent the three interior angles within a triangular grid cell.

[0043] The technical effect of the present invention is:

[0044] The present invention provides a method for predicting the grid quality of an electromagnetic calculation model based on a deep belief network. By randomly dividing multiple models with different grid densities and different triangular grid elements, a grid model sample library is established; then a grid quality evaluation index based on the grid density is established, and a deep belief network model is constructed. The grid quality evaluation index is used as the input data of the deep belief network model, and the root mean square error between the simulation result of the grid model sample and the reference result is used as the output of the deep belief network to train the deep belief network model; then, the object model to be electromagnetically calculated is meshed to obtain an estimated meshed model; the grid quality evaluation index of the estimated meshed model is calculated and used as the input data of the deep belief network model, and the prediction accuracy of the estimated meshed model is output. When the prediction accuracy meets the requirements, it indicates that the grid quality of the meshed model of the object model is good and can ensure the accuracy of electromagnetic numerical calculation.

[0045] Existing commercial electromagnetic simulation software can calculate the electromagnetic simulation results of a given model with relatively high calculation accuracy. However, researchers cannot know the electromagnetic parameters during the calculation process, which is not conducive to in-depth analysis of the electromagnetic characteristics of the given model. The method of the present invention can evaluate the influence of grid quality on the accuracy of electromagnetic numerical algorithms, and solves the problems in the prior art that the evaluation of the influence of grid quality on the accuracy of electromagnetic numerical algorithms relies on manual work and has low evaluation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solution of the present invention, the drawings required for the present invention will be briefly introduced below.

[0047] Figure 1 is a flow chart of the method of the present invention;

[0048] Figure 2 is a schematic diagram of the surface grid of a sphere model discretized with different grid densities;

[0049] Figure 3 is a schematic diagram of obtaining the RCS value of a sphere model by electromagnetic numerical calculation using the method of moments;

[0050] Figure 4 is a schematic diagram of the reference value of the radar cross section (Radar Scattering Sections, RCS) of a sphere model calculated using FEKO software;

[0051] Figure 5 The comparison chart of the RCS reference value of the sphere model and the RCS value obtained by the electromagnetic numerical algorithm;

[0052] Figure 6 It is the verification result of the deep belief network. Specific implementation mode

[0053] To make the above-mentioned objects, features and advantages of the present invention more obvious and understandable, the technical solutions of the present invention will be described completely and in detail below with reference to the drawings and embodiments.

[0054] This embodiment provides a method for predicting the grid quality of an electromagnetic calculation model based on a deep belief network. The process is as Figure 1 shown, including the following steps:

[0055] S1. Randomly divide a given number of object models to establish a grid model sample library;

[0056] For given spheres, cones, cylinders, etc., randomly divide the surfaces of each object model within a preset grid density range (0.5 - 0.8 wavelengths); extract the grid division node coordinates of different object models under different grid densities and different triangular grid element geometric indexes, and construct a grid model sample library.

[0057] For example, for the given sphere, its division cases at 0.8 wavelengths and 0.5 wavelengths are as Figure 2 shown. The divided triangular element grids are random and are non - equilateral triangle grids.

[0058] S2. Calculate the grid quality evaluation indexes of each divided model;

[0059] In this embodiment, the grid quality evaluation indexes include: element side length, element interior angle, element quality parameter, element twist angle; specifically,

[0060] The calculation formula of the element side length is:

[0061] edge = |v1| 2 +|v2| 2

[0062] where v1 and v2 respectively represent two vectors starting from the same node within the triangular grid element.

[0063] The calculation formula of the element interior angle is:

[0064]

[0065] The element quality parameter is:

[0066]

[0067] Among them, v1, v2, and v3 respectively represent three vectors within a triangular mesh cell.

[0068] The calculation formula for the unit twist angle is as follows:

[0069] θ skew = 90° - min(α1, α2, α3)

[0070] Among them, α1, α2, and α3 respectively represent the three interior angles within a triangular mesh cell.

[0071] S3. Calculate the error between the electromagnetic numerical calculation result and the reference result;

[0072] Using the method of moments as the electromagnetic numerical algorithm, calculate each meshed model in the meshed model sample library to obtain the electromagnetic numerical calculation results of all meshed models.

[0073] Use a commercial electromagnetic simulation software to calculate a given number of object models to obtain the reference results of each object model.

[0074] Compare the electromagnetic numerical calculation results of each meshed model with the corresponding reference results to obtain the root mean square error.

[0075] S4. Construct a deep belief network dataset;

[0076] Using the mesh quality evaluation indicators of all meshed models as input and the root mean square error corresponding to the meshed model as the label, construct a deep belief network dataset.

[0077] S5. Construct a deep belief network to determine the deep belief network structure, including the number of nodes and the number of layers; in this implementation, the number of nodes is 8 and the number of layers is 4.

[0078] Use the deep belief network dataset to test and verify the constructed deep belief network.

[0079] During the training process, set the network parameters of the deep belief network. Among them, the maximum number of iterations is set to 1000, the learning rate is set to 0.05, and the activation function S(x) and the loss function f(x) are respectively:

[0080]

[0081] f(x) = max(0, x)

[0082] Among them, the activation function is used to introduce non-linear capabilities, control the output range and gradient propagation, and enhance the generalization ability of the model. The loss function is used to quantify the model prediction error and guide the parameter optimization direction.

[0083] 100 samples from the deep belief network dataset were used for verification, and the verification results are as follows Figure 6 shown; as can be seen from the figure, the curves of the predicted values and the true values basically coincide, indicating that the root mean square error prediction accuracy obtained by predicting with the deep belief network model of the present invention is relatively high, that is, a trained deep belief network is obtained.

[0084] S6. Perform grid meshing on the metal conductor sphere, calculate the grid quality evaluation index of the meshed model, input the obtained grid quality evaluation index into the trained deep belief network, and output the prediction accuracy of the meshed model, and the meshed model meets the requirements of electromagnetic calculation.

[0085] Figure 3 The following shows the standard RCS value of the metal conductor sphere obtained by simulating with FEKO software; Figure 4 The following shows the RCS value obtained by performing electromagnetic calculation on the meshed model in step S6 using the method of moments; Figure 5 The following shows that the bistatic RCS results of the simulation results and the electromagnetic numerical algorithm are consistent, and the results calculated by the electromagnetic numerical algorithm are highly accurate.

[0086] In summary, the present invention can predict the grid quality of the meshed model. When the prediction accuracy meets the requirements, it indicates that the grid quality of the meshed model of the object model is good and can ensure the accuracy of electromagnetic numerical calculation.

[0087] The above content is only one implementation case of the present invention and does not constitute a limitation on the scope of patent protection of the present invention. Any equivalent structure or process transformation based on the description of the specification and drawings of the present invention, whether directly or indirectly applied to other related fields, is regarded as falling within the scope of patent protection of the present invention.

Claims

1. A method for predicting the grid quality of an electromagnetic calculation model based on a deep belief network, characterized in that, It includes the following steps: S1. Randomly divide a given plurality of object models to establish a grid model sample library; For a given plurality of object models, randomly divide the surfaces of each object model within a preset grid density range; Extract the grid division node coordinates of different object models under different grid densities and different triangular grid element geometric indexes, and construct a grid model sample library; S2. Calculate the grid quality evaluation indexes of each divided model; Select 4 parameters that affect the grid quality as the grid quality evaluation indexes; The 4 selected parameters are: element side length, element interior angle, element quality parameter, and element twist angle; S3. Calculate the error between the electromagnetic numerical calculation result and the reference result; Adopt the selected electromagnetic numerical algorithm to calculate each divided model in the grid model sample library to obtain the electromagnetic numerical calculation results of all divided models; Use a commercial electromagnetic simulation software to calculate a given plurality of object models to obtain the reference results of each object model; Compare and calculate the electromagnetic numerical calculation results of each divided model with the corresponding reference results to obtain the root mean square error; S4. Construct a deep belief network data set; Use the grid quality evaluation indexes of all divided models as inputs and the root mean square error corresponding to the divided models as labels to construct a deep belief network data set; S5. Construct a deep belief network structure; S6. For the object model to be electromagnetically calculated, perform grid division to obtain an estimated divided model; calculate the grid quality evaluation indexes of the estimated divided model as the input data of the deep belief network model, and output the prediction accuracy of the estimated divided model.

2. The method for predicting the grid quality of an electromagnetic calculation model based on a deep belief network according to claim 1, wherein In step S5, the method for constructing the deep belief network structure includes: Determine the deep belief network structure, including the number of nodes and the number of layers; the number of nodes and the number of layers are determined by the following formula: Among them, α is an arbitrary value variable that can be taken at will, and can take any integer between 1 and 10, N h is the number of neuron nodes in the hidden layer of the deep belief network structure, N i is the number of neuron nodes in the input layer of the hidden layer of the deep belief network structure, N o is the number of neuron nodes in the output layer of the hidden layer of the deep belief network structure; Use the deep belief network data set to test and verify the constructed deep belief network structure to obtain a trained deep belief network model.

3. The method for predicting the grid quality of an electromagnetic calculation model based on a deep belief network according to claim 2, wherein During the training process, set the network parameters of the deep belief network structure, including the maximum number of iterations, learning rate, activation function, and loss function. The activation function S(x) and the loss function f(x) are respectively: f(x) = max(0, x) where x represents the independent variable of the function.

4. The method for predicting the grid quality of an electromagnetic calculation model based on a deep belief network according to claim 3, wherein The calculation formula for the element side length is: edge = |v1| 2 + |v2| 2 where v1 and v2 respectively represent two vectors starting from the same node within a triangular grid element; the calculation formula for the element interior angle is: The element quality parameter is: where v1, v2, and v3 respectively represent the three vectors within a triangular grid element; The calculation formula for the element twist angle is: θ skew = 90° - min(α1, α2, α3) where α1, α2, and α3 respectively represent the three interior angles within a triangular grid element.

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