CN114330124A - Rapid simulation method for electromagnetic scattering characteristics of periodic target - Google Patents
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Abstract
The invention discloses a method for quickly simulating electromagnetic scattering characteristics of a periodic target, which comprises the following steps: generating a data set based on a traditional sub-universe basis function method; constructing an artificial neural network model; classifying the data set and training an artificial neural network model; and predicting the sub-global basis function expansion coefficient of the periodic array structure target by using the trained artificial neural network model, and completing the electromagnetic scattering induced current distribution calculation. The invention integrates the trained artificial neural network model into the sub-global basis function method, and rapidly predicts the expansion coefficient of the sub-global basis function, thereby avoiding the time-consuming cross-coupling reduction matrix equation solution, simplifying the original large-scale periodic array problem into a 3 multiplied by 3 small array problem containing 9 units, greatly reducing the simulation time and improving the calculation efficiency.
Description
Technical Field
The invention belongs to the technical field of electromagnetic calculation, and particularly relates to a periodic target electromagnetic scattering characteristic rapid simulation method based on an artificial neural network.
Background
In recent years, periodic structures have been widely used in phased array radar antennas, frequency selective surfaces, and metamaterials. As technology develops, the scale of the periodic structure becomes larger and larger, and in order to consider the marginal effect of the finite periodic structure, a large calculation load is generated by using a full-wave numerical calculation method. It is necessary to achieve rapid simulation for large scale finite period arrays.
The sub-universe base function method utilizes physical characteristics in a periodic structure, considers main coupling action in a 3 multiplied by 3 small array, and extracts three major types of nine minor types of sub-universe base functions by solving the small array, so that each unit in the array has only one base function, unknown quantity is greatly reduced, and the solving efficiency of a periodic structure target is improved. However, in this method, when a reduced matrix equation is established, the calculation complexity is the same as that of the conventional full-wave analysis method, so that it still takes time when the scale of the periodic structure becomes large. In addition, the sub-global basis function method needs to be recalculated once the array parameters are changed, which is disadvantageous for the rapid simulation of large-scale finite period structures.
In summary, further improvement and acceleration are still needed in the conventional sub-global basis function method.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects of the prior art, the invention provides a method for quickly simulating the electromagnetic scattering property of a periodic target, and the electromagnetic scattering property of a new array structure can be quickly estimated by calculating a limited number of periodic arrays, so that the calculation efficiency of a sub-universe basis function method is further improved.
The technical scheme is as follows: in order to achieve the above object, the invention provides a method for rapidly simulating electromagnetic scattering characteristics of a periodic target, comprising the following steps:
and 4, firstly extracting a 3 x 3 subarray from the periodic array structure target to be predicted to obtain sub-global basis functions, then generating corresponding network input parameters by each unit, predicting the sub-global basis function expansion coefficients of each unit by using a trained artificial neural network model, and finally obtaining the electromagnetic induction surface current distribution of the whole periodic array structure target.
Wherein the content of the first and second substances,
step 1.1, establishing a periodic array structure unit expansion direction of a data set in the + x-axis direction and the + y-axis direction, wherein the number of units in the + x-axis direction and the + y-axis direction ranges from 6 to 50, and the step length is 1, namely [6,7, …,50 ]; the period of each array is set to 0.6 to 1.2 wavelengths, step size is 0.1 wavelengths, i.e. [0.6,0.7, …,1.2 ];
step 1.2, coordinate (x) of central position of each unit in arrayi,yi) Center-to-center spacing between cells in an array (d)x,dy) And array size (N)x,Ny) As the input of each sample, the network input parameter (x) corresponding to the unit is obtained by combinationi,yi,dx,dy,Nx,Ny) The network input parameters of each unit form an input data set;
step 1.3, input data set standardization: carrying out standardization preprocessing on each column of an input data set matrix by using a Z-score standardization method, and compressing data to be between-1 and 1 after the Z-core standardization preprocessing;
and step 1.4, calculating the periodic array structure by using a traditional sub-global basis function method to obtain a sub-global basis function expansion coefficient of each unit, and dividing the expansion coefficient into an amplitude part and a phase part which serve as corresponding labels of the input data set.
The formula of the Z-score normalization method is as follows:
where μ and σ are the mean and standard deviation of the data, a represents the original value of the data, and a' represents the normalized value of the data.
2, the artificial neural network model consists of four layers including an input layer and three hidden layers, and the layers are in full connection; the first layer hidden layer adopts ReLU as an activation function, the second layer hidden layer adopts Tanh as an activation function, and the third layer hidden layer adopts ReLU as an activation function.
The input layer consists of 6 neurons, and the three hidden layers consist of 32, 28, and 20 neurons, respectively.
The artificial neural network model adopts an Adam optimizer as an optimizer of the model, a mean square loss function is used for calculating a loss value, and the learning rate is 0.01.
step 3.1, dividing the data set of the periodic array structure into three types, namely a central unit, an angle unit and an edge unit: classifying the internal units except the outermost unit into a data set of a central unit, classifying the 3 multiplied by 3 array at four corners into a data set of corner units, and classifying the peripheral three-layer unit into a data set of edge units;
3.2, randomly extracting 20% of samples in the data set as a verification set, and then using the rest samples as a training set and carrying out random disorder treatment to ensure that the trained model has certain generalization performance;
and 3.3, respectively carrying out artificial neural network model training on the central unit, the angle unit and the edge unit of the data set to obtain three sets of corresponding artificial neural network parameters.
3.3 the process of training the artificial neural network model comprises the following steps: through a data generator, a plurality of data in a training set are generated each time and are put into an artificial neural network model for training, all the training set data are trained once as one round to obtain the loss value of the training set, and then the data in a verification set are put into the artificial neural network model for testing to obtain the loss value of the verification set; and continuously adjusting network parameters through back propagation to enable loss values of the training set and the verification set to reach a set threshold range simultaneously, and then generating and storing a trained artificial neural network model.
The step 4 specifically comprises the following steps:
step 4.1, the scale of the periodic array to be predicted is N ═ Nx×NyExtracting 3 × 3 sub-arrays for analysis to obtain nine sub-universe basis functions
Step 4.2, aiming at the periodic array structure target to be predicted, generating corresponding network input parameters by each unit in the array, and carrying out standardization processing by using the average value mu and the standard deviation sigma used in Z-score standardization of the step 1.3 to obtain the network input parameters after standardization preprocessing;
step 4.3, inputting the network input parameters after the standardization pretreatment of each unit into the trained artificial neural network model, and predicting the expansion coefficient alpha of the corresponding sub-universe basis functioniThe value range of i is 1,2 … N;
step 4.4, obtaining the electromagnetic scattering induced current distribution of the periodic array to be predicted according to the following formula:
where r is the position vector of the observation point on the periodic array, Jtot(r) is the total current coefficient distribution of the array; mi is the location, root, of the cellThe classification of the cells in the sub-population basis function method corresponds to 1,2, …, 9;
is the sub-global SED basis function of the cell at the mi location, K is the number of RWG basis functions per cell,
for the l RWG basis function on the cell,
representing a field point;
is RWG basis function coefficient vector I on a 3 × 3 sub-arraySEDRow mi and column l.
Step 4.1, extracting the 3 × 3 subarray for analysis to obtain nine types of sub-universe basis functions
The specific process is as follows:
obtaining a matrix equation based on RWG basis functions, an electric field integral equation and Galerkin test:
ZSEDISED＝VSED (4)
wherein Z isSEDIs an impedance matrix, ISEDIs a RWG basis function coefficient vector, V, over a 3 × 3 sub-arraySEDA voltage vector of a 3 × 3 sub-array;
impedance matrix ZSEDM-th row and n-column elements
Comprises the following steps:
wherein the content of the first and second substances,
respectively representing a field point and a source point,
RWG basis functions at a field point and a source point, respectively, j is an imaginary unit, k is a wave constant in free space, η is a free space wave impedance,
the Green function is a free space, and the expression is as follows:
by solving equations (4), (5) and (6), we obtain:
in the formula (I), the compound is shown in the specification,
the nine types of sub-global basis functions are represented, wherein the four types of sub-global basis functions comprise four corner units, four edge units and a central unit.
Has the advantages that: compared with the prior art, the invention has the following beneficial effects:
the method mainly learns the distribution of the universe base function on the periodic structure through the artificial neural network, so that a new array structure can be quickly simulated, and other scale periodic structures can be predicted by calculating a limited number of periodic structures and training an artificial neural network model; through the artificial neural network, the expansion coefficient of the sub-universe basis function can be rapidly predicted with extremely high efficiency, and the efficiency is high.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of constructing an array of data sets;
FIG. 3 is a schematic diagram of an input parameter format;
FIG. 4 is a schematic diagram of an artificial neural network model;
FIG. 5 is a schematic diagram of the classification of the elements of the constructed data set array;
FIG. 6 is a schematic diagram of a 40 × 40 square periodic structure;
FIG. 7 is a cross-sectional diagram of a dual-station radar with normal incidence plane wave calculated by the method of the present invention using the moment method, the conventional sub-global basis function, and the periodic structure of the embodiment at 300 MHz;
FIG. 8 is a cross-sectional diagram of a dual-station radar with normal incidence plane wave calculated by the method of the present invention using the moment method, the conventional sub-gamut basis function and the method of the present invention for a 100 × 100 square periodic structure at 300 MHz.
Detailed Description
To further illustrate the practice of the method of the present invention, reference is made to the following description taken in conjunction with the accompanying drawings and examples.
The invention discloses a method for rapidly simulating electromagnetic scattering characteristics of a periodic target, which comprises the following steps of:
step 1.1, setting the array unit expansion directions for establishing the data set as the + x-axis direction and the + y-axis direction. The range along the + x-axis direction and the + y-axis direction is 6 to 30 with a step size of 1, i.e., [6,7, …,50 ]. The period of each array is set to 0.6 to 1.2 wavelengths with a step size of 0.1 wavelengths, i.e. [0.6,0.7, …,1.2 ]. By setting, 315 arrays can be obtained.
Step 1.2, as shown in FIG. 2, based on the position parameter (x) of each cell in the arrayi,yi) The spacing between the cells in the array (d)x,dy) And array size (N)x,Ny) As an input for each sample; as shown in fig. 3, byThe combination can obtain the network input parameter (x) corresponding to the uniti,yi,dx,dy,Nx,Ny)。
And step 1.3, because large span exists among different types of parameter values, convergence is difficult to perform during artificial neural network model training. Here, a Z-core normalization method is applied to pre-process each column of the input dataset matrix, i.e., each class of parameters. The formula for Z-core normalization is as follows:
where μ and σ represent the mean and standard deviation of the data, respectively, a represents the original value of the data, and a' represents the normalized value of the data.
After Z-core standardization, the data can be compressed to be between-1 and 1, and the training of the artificial neural network model is facilitated.
Step 1.4, calculating the extension coefficient of the sub-global basis function on each unit as the corresponding output (inputting the corresponding label) by using the sub-global basis function method, and because the extension coefficient is complex and the neural network can only process real numbers, the extension coefficient is split into amplitude and phase as the output, that is, the extension coefficient is split into amplitude and phase as the output
the artificial neural network model consists of four layers including an input layer and three hidden layers, and the layers are in full connection; as shown in fig. 4, based on back propagation, an artificial neural network model including 3 hidden layers is established, a first hidden layer adopts ReLU as an activation function, a second hidden layer adopts Tanh as an activation function, and a third hidden layer adopts ReLU as an activation function; the input layer has 6 neurons, and the hidden layer consists of 32+28+20 neurons.
When the loss value is calculated, a mean square loss function is adopted, an Adam optimizer is adopted as an optimizer of the artificial neural network model, the learning rate is set to be 0.01, and the number of training rounds is 10000.
step 3.1, dividing the periodic array structure data set into three types, namely a central unit, an angle unit and an edge unit: as shown in fig. 5, the inner cells except the outermost cell are classified as the training set of the center cell, the small arrays of 3 × 3 at the four corners are classified as the training set of the corner cells, and the peripheral three-layer cells are classified as the training set of the edge cells.
3.2, randomly extracting 20% of samples in the preprocessed data set as a verification set, and then using the rest samples as a training set and performing random disorder processing to ensure that the trained model has certain generalization performance;
3.3, respectively carrying out artificial neural network model training on the central unit, the angle unit and the edge unit of the periodic array structure to obtain three sets of corresponding artificial neural network parameters: and through a data generator, a plurality of data in the training set are generated each time and are put into an artificial neural network model for training, all the training set data are trained once as one round to obtain the loss value of the training set, and then the data in the verification set are put into the model for testing to obtain the loss value of the verification set. Inputting the preprocessed verification set data into the trained model to obtain predicted data, and comparing the predicted data with the real output value of the verification set to judge the generalization performance of the model. And continuously adjusting and optimizing network parameters through back propagation to ensure that the loss values of the training set and the verification set reach a lower range at the same time, and then generating and storing a trained artificial neural network model.
And 4, predicting a sub-global basis function expansion coefficient of the periodic array structure target by using the trained artificial neural network model, and completing electromagnetic scattering induced current distribution calculation, wherein the method specifically comprises the following steps:
step 4.1, the scale of the periodic array to be predicted is N ═ Nx×NyExtracting a 3 multiplied by 3 small array for analysis, and obtaining a matrix equation based on RWG (Rao-Wilton-Glisson) basis functions, an electric field integral equation and a Galerkin test:
ZSEDISED＝VSED (2)
wherein Z isSEDIs an impedance matrix, ISEDIs a RWG basis function coefficient vector, V, over a 3 × 3 sub-arraySEDA voltage vector of a 3 × 3 sub-array;
impedance matrix ZSEDRow m and column n elements of (1)
Comprises the following steps:
wherein the content of the first and second substances,
respectively representing a field point and a source point,
RWG basis functions at a field point and a source point, respectively, j is an imaginary unit, k is a wave constant in free space, η is a free space wave impedance,
the Green function is a free space, and the expression is as follows:
by solving the above matrix equation, one can obtain:
in the formula (I), the compound is shown in the specification,
corresponding to nine types of sub-global basis functions, there are four corner units, four edge units and a central unit.
And 4.2, aiming at the array to be predicted, generating corresponding network input parameters by each unit in the array, and carrying out preprocessing standardization on the newly generated input parameters by using the average value mu and the standard deviation sigma used in the standardization of the data set Z-core in the step 1.3.
Step 4.3, inputting the network input parameters preprocessed by each unit into the trained artificial neural network model, determining the position of the unit to be predicted in the array by the artificial neural network model according to the input parameters, adaptively switching the network parameters of the corresponding unit types, and predicting the expansion coefficient alpha of the corresponding sub-global basis functioniAnd i has a value range of 1,2 … N. Finally, the electromagnetic scattering induced current distribution of the entire array can be obtained:
wherein, Jtot(r) is the total current coefficient distribution of the array, r is the position vector of the observation points on the periodic array; mi is the location of the unit, corresponding to 1, 2.., 9 according to the classification of the unit in the sub-global basis function method;
is the SED (sub-global) basis function of the cell at the mi position, and the calculation method is shown as the formula (3). K is the number of RWG basis functions per cell,
is the l RWG basis function on the cell;
is RWG basis function coefficient vector I on a 3 × 3 sub-arraySEDRow mi and column l.
Then, according to the relation between the current and a Radar Cross Section (RCS) tau, calculating to obtain the Radar Cross section of the array:
wherein E isscaIn the form of a scattered field, the magnetic field,
and
is field point to source point, r is field point to source point distance, ω is angular velocity, μ0Is the permeability in air.
In order to verify the accuracy and the high efficiency of the invention, the following takes the analysis of the square cell array structure as an example, and the example is completed on a personal computer with the main frequency of 2.8GHz, the memory of 32GB, the video card of GTX1060 and the video memory of 6 GB.
As shown in FIG. 6, a 40 × 40 square periodic array of cells with a solution frequency of 300MHz, a wavelength λ of 1 m, a cell side length of 0.5 λ, and a cell center-to-center distance dx＝dy0.9 λ. The polarization direction of the incident plane wave is the-x axis, the amplitude is 1V, and the propagation direction is from the + z axis to the-z axis.
Fig. 7 shows radar scattering cross section distribution diagrams of embodiments calculated by the conventional sub-gamut basis function method and the method of the present invention, and it can be seen that the coincidence degree of the two methods is high.
FIG. 8 shows the comparison of the distribution of the scattering cross-section of the radar with an array scale of 100X 100 and a unit center spacing of 0.7 lambda, the calculation methods being the moment method and the method of the invention, respectively. It can be seen that the two methods keep high goodness of fit, and the accuracy of the method is proved.
Table 1 shows the moment method, the conventional sub-gamut basis function method, and the time consumption required for the calculation embodiment of the method of the present invention, and it can be seen that the time consumption of the method of the present invention is very small compared to the conventional method, thereby proving the high efficiency of the method of the present invention.
TABLE 1 moment method, conventional sub-gamut basis function method, and time consumption required to calculate embodiments of the method of the present invention
The foregoing illustrates the general principles, principal features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are merely illustrative of the principles of the invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (10)
1. A method for rapidly simulating electromagnetic scattering characteristics of a periodic target is characterized by comprising the following steps:
step 1, generating a data set based on a traditional sub-universe basis function method: constructing a series of periodic array structures with different unit pitches and different scales, calculating to obtain an expansion coefficient of a sub-global basis function on each unit based on a traditional sub-global basis function method, taking the unit and array information where the unit is located as the input of a data set, and taking the expansion coefficient of the sub-global basis function as a tag of the data set;
step 2, constructing an artificial neural network model based on back propagation;
step 3, classifying the data set, and training an artificial neural network model: dividing a data set into three types, namely a central unit, an angle unit and an edge unit, and respectively training three sets of artificial neural network parameters;
and 4, firstly extracting a 3 x 3 subarray from the periodic array structure target to be predicted to obtain sub-global basis functions, then generating corresponding network input parameters by each unit, predicting the sub-global basis function expansion coefficients of each unit by using a trained artificial neural network model, and finally obtaining the electromagnetic induction surface current distribution of the whole periodic array structure target.
2. The method for rapidly simulating the electromagnetic scattering property of a periodic target according to claim 1, wherein the step 1 of generating the data set based on the conventional sub-global basis function method comprises the following steps:
step 1.1, establishing a periodic array structure unit expansion direction of a data set in the + x-axis direction and the + y-axis direction, wherein the number of units in the + x-axis direction and the + y-axis direction ranges from 6 to 50, and the step length is 1, namely [6,7, …,50 ]; the period of each array is set to 0.6 to 1.2 wavelengths, step size is 0.1 wavelengths, i.e. [0.6,0.7, …,1.2 ];
step 1.2, coordinate (x) of central position of each unit in arrayi,yi) Center-to-center spacing between cells in an array (d)x,dy) And array size (N)x,Ny) As the input of each sample, the network input parameter (x) corresponding to the unit is obtained by combinationi,yi,dx,dy,Nx,Ny) The network input parameters of each unit form an input data set;
step 1.3, input data set standardization: carrying out standardization preprocessing on each column of an input data set matrix by using a Z-score standardization method, and compressing data to be between-1 and 1 after the Z-core standardization preprocessing;
and step 1.4, calculating the periodic array structure by using a traditional sub-global basis function method to obtain a sub-global basis function expansion coefficient of each unit, and dividing the expansion coefficient into an amplitude part and a phase part which serve as corresponding labels of the input data set.
3. The method for rapidly simulating the electromagnetic scattering property of a periodic target according to claim 2, wherein the formula of the Z-score normalization method is as follows:
where μ and σ are the mean and standard deviation of the data, a represents the original value of the data, and a' represents the normalized value of the data.
4. The method for rapidly simulating the electromagnetic scattering property of the periodic target according to claim 1, wherein the artificial neural network model in the step 2 is composed of four layers including an input layer and three hidden layers, and the layers are fully connected; the first layer hidden layer adopts ReLU as an activation function, the second layer hidden layer adopts Tanh as an activation function, and the third layer hidden layer adopts ReLU as an activation function.
5. The method for rapidly simulating the electromagnetic scattering properties of a periodic object as claimed in claim 4, wherein said input layer is composed of 6 neurons, and said three hidden layers are respectively composed of 32, 28 and 20 neurons.
6. The method for rapidly simulating the electromagnetic scattering property of the periodic target as claimed in claim 1 or 4, wherein the artificial neural network model adopts an Adam optimizer as an optimizer of the model, a mean square loss function is used for calculating a loss value, and the learning rate is 0.01.
7. The method for rapidly simulating the electromagnetic scattering property of the periodic target according to claim 1, wherein the step 3 of classifying the data set and training the artificial neural network model comprises the following steps:
step 3.1, dividing the data set of the periodic array structure into three types, namely a central unit, an angle unit and an edge unit: classifying the internal units except the outermost unit into a data set of a central unit, classifying the 3 multiplied by 3 array at four corners into a data set of corner units, and classifying the peripheral three-layer unit into a data set of edge units;
3.2, randomly extracting 20% of samples in the data set as a verification set, and then using the rest samples as a training set and carrying out random disorder treatment to ensure that the trained model has certain generalization performance;
and 3.3, respectively carrying out artificial neural network model training on the central unit, the angle unit and the edge unit of the data set to obtain three sets of corresponding artificial neural network parameters.
8. The method for rapidly simulating the electromagnetic scattering property of the periodic target according to claim 7, wherein the step 3.3 of performing the artificial neural network model training comprises the following steps: through a data generator, a plurality of data in a training set are generated each time and are put into an artificial neural network model for training, all the training set data are trained once as one round to obtain the loss value of the training set, and then the data in a verification set are put into the artificial neural network model for testing to obtain the loss value of the verification set; and continuously adjusting network parameters through back propagation to enable loss values of the training set and the verification set to reach a set threshold range simultaneously, and then generating and storing a trained artificial neural network model.
9. The method for rapidly simulating the electromagnetic scattering property of the periodic target according to claim 1, wherein the step 4 specifically comprises the following steps:
step 4.1, the scale of the periodic array to be predicted is N ═ Nx×NyExtracting 3 × 3 sub-arrays for analysis to obtain nine sub-universe basis functions
Step 4.2, aiming at the periodic array structure target to be predicted, generating corresponding network input parameters by each unit in the array, and carrying out standardization processing by using the average value mu and the standard deviation sigma used in Z-score standardization of the step 1.3 to obtain the network input parameters after standardization preprocessing;
step 4.3, inputting the network input parameters after the standardization pretreatment of each unit into the trained artificial neural network model, and predicting the expansion coefficient alpha of the corresponding sub-universe basis functioniThe value range of i is 1,2 … N;
step 4.4, obtaining the electromagnetic scattering induced current distribution of the periodic array to be predicted according to the following formula:
where r is the position vector of the observation point on the periodic array, Jtot(r) is the total current coefficient distribution of the array; mi is the location of the cell, which corresponds to 1,2, …,9 according to the classification of the cell in the sub-population basis function method;
is the sub-global SED basis function of the cell at the mi location, K is the number of RWG basis functions per cell,
for the l RWG basis function on the cell,
representing a field point;
is RWG basis function coefficient vector I on a 3 × 3 sub-arraySEDRow mi and column l.
10. The method for rapidly simulating the electromagnetic scattering property of the periodic target according to claim 1, wherein in step 4.1, 3 x 3 sub-arrays are extracted and analyzed to obtain nine types of sub-global basis functions
The specific process is as follows:
obtaining a matrix equation based on RWG basis functions, an electric field integral equation and Galerkin test:
ZSEDISED＝VSED (4)
wherein Z isSEDIs an impedance matrix, ISEDIs a RWG basis function coefficient vector, V, over a 3 × 3 sub-arraySEDA voltage vector of a 3 × 3 sub-array;
impedance matrix ZSEDM-th row and n-column elements
Comprises the following steps:
wherein the content of the first and second substances,
respectively representing a field point and a source point,
RWG basis functions at a field point and a source point, respectively, j is an imaginary unit, k is a wave constant in free space, η is a free space wave impedance,
the Green function is a free space, and the expression is as follows:
by solving equations (4), (5) and (6), we obtain:
in the formula (I), the compound is shown in the specification,
the nine types of sub-global basis functions are represented, wherein the four types of sub-global basis functions comprise four corner units, four edge units and a central unit.
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