VLF propagation signal prediction method based on three-dimensional finite element and neural network

Abstract

The invention discloses a VLF propagation signal prediction method based on a three-dimensional finite element and a neural network, and belongs to the technical field of electronic communication. The method comprises the following steps: firstly, constructing a geosphere-ionosphere waveguide model based on a three-dimensional frequency domain finite element method, and solving by using a multi-grid method to improve the operation efficiency; secondly, constructing a VLF signal propagation data set of a plurality of known paths at one time based on a three-dimensional frequency domain finite element method; then, constructing a neural network model reflecting a mapping relation between an ionized layer electron density parameter and a VLF wave characteristic based on the data set; then, obtaining electron density distribution on a plurality of known paths based on neural network inversion; and finally, carrying out inversion by adopting an inverse square weight formula to obtain electron density distribution on the to-be-solved path. According to the method, the VLF signal transmission characteristics on multiple paths can be simulated at a time, the workload of modeling simulation is effectively reduced, and the method is suitable for the fields of inversion of a multi-path electron density parameter model, prediction of very low frequency wave propagation and the like.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electronic communication, and relates to a VLF propagation signal prediction method based on three-dimensional finite elements and neural networks. BACKGROUND

[0002] Currently, navigation and communication systems face many challenges in complex electromagnetic environments. The global navigation system has signal blind areas in underground or deep sea areas, and underwater communication has problems of insufficient resolution and penetration ability. Very low frequency (VLF, 3-30 kHz) electromagnetic waves have super-long propagation distance, strong penetration ability and strong anti-interference electromagnetic characteristics, and show irreplaceable advantages in global navigation and underwater communication. The modeling method of full-wave simulation significantly reduces the cost of field test and provides experimental support for in-depth study of VLF waves.

[0003] Current VLF propagation numerical simulation methods face significant limitations in balancing calculation efficiency and accuracy. Although the long-wave propagation characteristic model (LWPC) is fast in calculation, it cannot handle three-dimensional mode coupling effects. The three-dimensional frequency domain finite element method (FEM) can effectively simulate the mode coupling and interference of waveguide propagation. Compared with the time domain finite difference method (FDTD), the three-dimensional frequency domain finite element method is fast in calculation. At present, there are few studies on VLF ground-ionospheric waveguide propagation based on the three-dimensional frequency domain finite element method, especially in terms of VLF wave propagation characteristics on multiple paths simulated at one time.

[0004] Neural networks have shown great potential in VLF propagation modeling and prediction, and can effectively solve complex nonlinear problems. Neural networks can establish a mapping relationship between electron density and VLF signal amplitude and phase changes through nonlinear fitting. In 2019, Gross et al. (VLF Remote Sensing of the D Region Ionosphere Using Neural Networks) trained artificial neural networks (ANN) with LWPC simulation data, and predicted the propagation characteristics of unknown paths with adjacent path electron density data. The prediction error is large compared with the true value. In the invention patent named "Method for Inverting Low Ionosphere Electron Density Based on Neural Network and Genetic Algorithm", the genetic algorithm is introduced to output the improved IRI electron density profile that meets the measured VLF propagation characteristics, but this method has the problems of slow operation speed and multiple output variables. It is still necessary to further study the development of three-dimensional frequency domain finite element method and the introduction of neural networks to quickly and efficiently predict the VLF wave propagation characteristics of unknown paths with existing VLF data.

[0005] The prior art has the problems of incompatible calculation efficiency and accuracy, high dependence on measured data, and inability to simultaneously predict VLF wave propagation characteristics of multiple paths. SUMMARY

[0006] The present application proposes a VLF propagation signal prediction method based on three-dimensional finite elements and neural networks to solve the problems raised in the background art. The present application method can simulate the VLF signal transmission characteristics of multiple paths at one time, effectively reducing the workload of modeling and simulation compared to traditional two-dimensional finite element models, and can simulate mode coupling and interference of waveguide propagation.

[0007] The technical scheme adopted by the present application is as follows:

[0008] A VLF propagation signal prediction method based on three-dimensional finite elements and neural networks, comprising the following steps:

[0009] S1. Construct a three-dimensional ground-ionospheric waveguide model of the VLF electromagnetic wave transmission path;

[0010] S2. Construct a VLF signal propagation dataset based on a three-dimensional frequency domain finite element method;

[0011] S21. Construct multiple VLF signal propagation paths and set the electron density spatial gradient β and characteristic scale H distribution on the VLF signal propagation path; introduce the electron density spatial gradient β and characteristic scale H into the three-dimensional ground-ionospheric waveguide model established in step S1 to obtain a three-dimensional ground-ionospheric waveguide model containing electron density distribution;

[0012] S22. Solve the three-dimensional Earth-ionosphere waveguide model containing electron density distribution to obtain the transmission characteristics of very low frequency electromagnetic waves; construct a VLF signal propagation dataset based on the propagation characteristics of very low frequency electromagnetic waves;

[0013] S3. Build a neural network model and then, based on the VLF signal propagation dataset, construct a mapping relationship between the ionospheric D region electron density model parameters and the VLF wave amplitude and phase. The ionospheric D region electron density model parameters include: electron density spatial gradient β and characteristic scale H.

[0014] S4. Obtain electron density distributions along at least three known paths based on neural network inversion;

[0015] S5. Substitute the electron density distribution on the known path obtained in step S4 into the inverse square weight formula, and invert to obtain the electron density distribution on the path to be determined.

[0016] The beneficial effects of the present invention are as follows:

[0017] The method of the present invention first constructs an Earth-ionosphere waveguide model based on the three-dimensional frequency-domain finite element method, and uses a multi-grid solution to improve computational efficiency. Secondly, a VLF signal propagation dataset for multiple known paths is constructed at once based on the three-dimensional frequency-domain finite element method. Next, a neural network model is constructed based on the dataset to reflect the mapping relationship between ionospheric electron density parameters and VLF wave characteristics. Then, the electron density distribution on several known paths is obtained based on neural network inversion. Finally, the electron density distribution on the path to be determined is obtained by inversion using the inverse square weight formula. The method of the present invention can simulate the VLF signal transmission characteristics on multiple paths at once, effectively reducing the workload of modeling and simulation. It is suitable for fields such as the inversion of multi-path electron density parameter models and the prediction of very low frequency wave propagation. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Comparison of simulation results of the three-dimensional Earth-ionosphere waveguide model and the traditional two-dimensional finite element model on the same path in the embodiment;

[0019] Figure 2 This is a flow chart of a method for predicting VLF propagation characteristics based on three-dimensional finite element and neural network in an embodiment;

[0020] Figure 3 The training results of the CNN-LSTM neural network model in the embodiment;

[0021] Figure 4 The electron density β and H parameters of NML to BD, BW and OX are inverted based on neural network in the embodiment;

[0022] Figure 5The electron density β and H parameters on the NML to BX path are constructed based on the inverse square weight formula in the embodiment;

[0023] Figure 6 Comparison between the experimental measured and predicted values ​​of the magnetic flux density amplitude and phase on the NML to BX path in the embodiment. DETAILED DESCRIPTION

[0024] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] S1. Constructing a three-dimensional Earth-ionosphere waveguide model for very low frequency electromagnetic wave transmission paths

[0026] Determine the longitude and latitude of one transmitting point and ten receiving points; use the coordinate transformation formula to obtain the positions of all transmitting points and receiving points in the rectangular coordinate system, calculate the direction of the electric dipole moment of the transmitting point, and establish a three-dimensional Earth-ionosphere waveguide model.

[0027] The coordinate transformation formula is as follows:

[0028] x=a×cos(u)×cos(L) (1)

[0029] y=a×cos(u)×sin(L) (2)

[0030] z=a×sin(u) (3)

[0031] Where a is the radius of the earth, u and L are the latitude and longitude of the transmitting and receiving points respectively, and x, y, and z are the three components of the transmitting and receiving points in the rectangular coordinate system respectively.

[0032] S2. Constructing a VLF signal propagation dataset based on the three-dimensional frequency domain finite element method

[0033] S21. Construct ten VLF signal propagation paths and set the electron density spatial gradient β and characteristic scale H distribution on the VLF signal propagation paths so that the ionospheric electron density on each path varies differently with time and space; introduce the electron density spatial gradient β and characteristic scale H into the three-dimensional Earth-ionosphere waveguide model established in step S1 to obtain a three-dimensional Earth-ionosphere waveguide model containing electron density distribution.

[0034] S22. Solve the three-dimensional Earth-ionosphere waveguide model with electron density distribution based on V-Cycle multigrid.

[0035] The medium parameters and boundary conditions of the three-dimensional Earth-ionosphere waveguide model containing electron density distribution are discretized to generate the coefficient matrix A h , where the subscript h is the grid size; let the solution vector u hUsed to characterize the discretized electric field components Ex, Ey, Ez and magnetic field components Hx, Hy, Hz, f h Represents the excitation source, and the linear equations are expressed as:

[0036] A h u h =f h (4)

[0037] By solving the above linear equations, the transmission characteristics of very low frequency electromagnetic waves are obtained.

[0038] The solution process is as follows:

[0039] Eliminate high-frequency errors in the linear equations by smoothing iteration (Gauss-Seidel) and calculate the residual r h for:

[0040] r h =f h -A h u h (5)

[0041] Using the error estimate e 2h The residual r h Transfer to coarse grid A 2h :

[0042] A 2h e 2h =r 2h (6)

[0043] Using the restriction operator I h 2h Then the error estimate e 2h Interpolate back to the fine grid to correct the solution vector u h :

[0044]

[0045] Corrected solution vector u h After smoothing again, one V-Cycle iteration is completed;

[0046] Solution vector u h Repeat multiple times until the error estimate e 2h Less than the set threshold, the solution vector u containing the electric field components Ex, Ey, Ez and the magnetic field components Hx, Hy, Hz is obtained. h .

[0047] The amplitudes and phases of the electric and magnetic field components of the VLF signals along the propagation paths are extracted to construct a VLF signal propagation dataset. In this embodiment, 1000 sets of amplitude and phase values ​​are extracted along each of the three paths to construct three VLF signal propagation datasets. Therefore, each VLF signal propagation dataset for a known path contains 1000 sets of data.

[0048] Figure 1 The VLF signal propagation curve along the same path for the three-dimensional Earth-ionosphere waveguide model of the present invention and the traditional two-dimensional finite element model is shown in the figure. The length, width and height of the three-dimensional model are 1000km×300km×120km. In the direction perpendicular to the propagation path, the VLF propagation curve tends to converge when the width of the three-dimensional model reaches 300km or more. Figure 1 It can be seen that the calculation results of the two methods are basically consistent, which shows that the three-dimensional Earth-ionosphere waveguide model established by the present invention can accurately solve the propagation characteristics of VLF signals.

[0049] S3. Construct a neural network model based on the VLF signal propagation dataset to build a mapping relationship between the ionospheric D region electron density model parameters and the VLF wave amplitude and phase.

[0050] A CNN-LSTM neural network model is constructed, and the first 900 groups of data in the VLF signal propagation dataset extracted on each known path in step S2 are used as training sets, and the last 100 groups of data are used as test sets. Figure 2 Flowchart of the method for predicting VLF propagation characteristics based on three-dimensional finite element and neural network.

[0051] The amplitude and phase of each set of data in each training set are used as the input of the three neural network models, and β and H are used as the output. The three CNN-LSTM neural network models are trained separately; the trained CNN-LSTM neural network models can reflect the mapping relationship between the amplitude and phase of the VLF signal of the ionospheric β and H parameters on the three paths.

[0052] In the test set, 10 groups of data were selected to test the CNN-LSTM neural network model. The results are as follows Figure 3 As shown, the predicted value and the set value trend are well synchronized.

[0053] S4. Inversion of the true electron density distribution on a known path based on a CNN-LSTM neural network

[0054] The transmitting point transmits a very low frequency signal, and the very low frequency signals actually received by any three receiving points in step S2 are obtained; the amplitude and phase of the received very low frequency signal are extracted and input into the CNN-LSTM neural network model of the corresponding path, and the electron density distribution on the three paths is inverted.

[0055] This implementation case is based on the amplitude and phase of the 25.2 kHz VLF signal received by BD, BW, and OX stations from NML station. Figure 4 (a) and Figure 4 (b) The electron density distribution inverted by the trained CNN-LSTM neural network model on three known paths is given respectively.

[0056] S5. Inverse the electron density distribution on the path to be determined based on the inverse square weight formula

[0057] Solve the predicted electron density parameter β on the path to be solved based on the inverse square weight formula x and H x :

[0058]

[0059] Among them, d i represents the distance from the receiving point of the i-th known path to the receiving point of the path to be determined, β i 、H i represent the electron density spatial gradient and characteristic scale on the i-th known path respectively.

[0060] Figure 5 The real electron density parameter β of the ionosphere on the path to be determined (the transmitting point is NML and the receiving point is BX) is given based on the inverse square weight method. x and H x .

[0061] The following comparative experimental test data verifies the prediction accuracy of the present invention

[0062] Figure 6 (a) and Figure 6 (b) Comparison of the experimental measured and predicted values ​​of the magnetic flux density amplitude and phase on the BX path. The inverted ionospheric electron density β on the BX path is x and H x The parameters were introduced into a three-dimensional Earth-ionosphere waveguide model, with an electric dipole as the excitation source and an electric dipole moment amplitude of 2 A·m. The predicted amplitude and phase along the path under investigation were consistent with the actual values ​​obtained from experimental measurements, demonstrating the accuracy of the proposed VLF propagation signal prediction method based on three-dimensional finite elements and neural networks.

Claims

1. A VLF propagation signal prediction method based on three-dimensional finite element and neural network, characterized in that: The following steps are involved: S1. Construct a three-dimensional Earth-ionosphere waveguide model of the very low frequency electromagnetic wave transmission path; S2. Construct a VLF signal propagation dataset based on the three-dimensional frequency domain finite element method; S21. Constructing multiple VLF signal propagation paths and setting the electron density spatial gradient β and characteristic scale H distribution on the VLF signal propagation paths; introducing the electron density spatial gradient β and characteristic scale H into the three-dimensional Earth-ionosphere waveguide model established in step S1 to obtain a three-dimensional Earth-ionosphere waveguide model containing the electron density distribution; S22. Solve the three-dimensional Earth-ionosphere waveguide model containing electron density distribution to obtain the transmission characteristics of very low frequency electromagnetic waves; construct a VLF signal propagation dataset based on the propagation characteristics of very low frequency electromagnetic waves; S3. Build a neural network model and then, based on the VLF signal propagation dataset, construct a mapping relationship between the ionospheric D region electron density model parameters and the VLF wave amplitude and phase. The ionospheric D region electron density model parameters include: electron density spatial gradient β and characteristic scale H. S4. Obtain electron density distributions along at least three known paths based on neural network inversion; S5. Substitute the electron density distribution on the known path obtained in step S4 into the inverse square weight formula, and invert to obtain the electron density distribution on the path to be determined.

2. The VLF propagation signal prediction method based on three-dimensional finite element and neural network according to claim 1, characterized in that: In step S1, a three-dimensional Earth-ionosphere waveguide model of a very low frequency electromagnetic wave transmission path is constructed by determining the longitude and latitude of a transmitting point and multiple receiving points; using a coordinate transformation formula to obtain the positions of all transmitting points and receiving points in a rectangular coordinate system, and calculating the direction of the electric dipole moment of the transmitting point to establish a three-dimensional Earth-ionosphere waveguide model.

3. The VLF propagation signal prediction method based on three-dimensional finite element and neural network according to claim 1 or 2, characterized in that: In step S22, the V-Cycle multi-grid numerical calculation method is used to solve the three-dimensional Earth-ionosphere waveguide model containing electron density distribution.

4. The VLF propagation signal prediction method based on three-dimensional finite element and neural network according to claim 3, characterized in that: In step S22, the solution process is as follows: Eliminate high-frequency errors in the linear equations by smoothing iteration and calculate the residual r h for: r h =f h -A h u h Using the error estimate e 2h The residual r h Transfer to coarse grid A 2h : A 2h e 2h =r 2h Using the restriction operator I h 2h Then the error estimate e 2h Interpolate back to the fine grid to correct the solution vector u h : Corrected solution vector u h After smoothing again, one V-Cycle iteration is completed; Solution vector u h Repeat multiple times until the error estimate e 2h Less than the set threshold, the solution vector u containing the electric field components Ex, Ey, Ez and the magnetic field components Hx, Hy, Hz is obtained. h .

5. The VLF propagation signal prediction method based on three-dimensional finite element and neural network according to claim 4, characterized in that: In step S4, the electron density distribution on the known path is obtained based on the neural network inversion as follows: Instructing the transmitting point to transmit a very low frequency signal, and obtaining the very low frequency signals actually received by at least three receiving points in step S2; The amplitude and phase of the received very low frequency signal are extracted and input into the CNN-neural network model of the corresponding path, and the electron density distribution on the three paths is inverted.

6. The VLF propagation signal prediction method based on three-dimensional finite element and neural network according to claim 5, characterized in that: In step S5, the inverse square weight formula is as follows: Among them, d i represents the distance from the receiving point of the i-th known path to the receiving point of the path to be determined, β x 、H x They represent the electron density spatial gradient and characteristic scale on the path to be determined, β i 、H i represent the electron density spatial gradient and characteristic scale on the i-th known path respectively.

7. The VLF propagation signal prediction method based on three-dimensional finite element and neural network according to claim 5, characterized in that: The neural network model in step S3 is a CNN-LSTM neural network model.

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