A method and system for predicting low-frequency ground wave propagation characteristics of partitioned hybrid paths

Abstract

The present invention belongs to the technical field of radio wave propagation, and specifically discloses a method and system for predicting the propagation characteristics of low-frequency ground waves in partitioned hybrid paths. The method of the present invention first inputs model parameters; then uses the flat ground formula to obtain the initial field distribution of the parabolic equation at the initial position; then uses the SSFT algorithm combining DMFT and FFT to solve 3DPE; finally, uses the field results in the entire calculation area to calculate the magnetic field intensity and quadratic time delay of radio wave propagation. The method of the present invention solves the problem that the lateral wave propagation of low-frequency ground waves is affected by the two-dimensional parabolic equation method because it does not consider the irregular intersection between hybrid paths, and overcomes the singularity caused by the reflection coefficient of the SSFT algorithm based on field parity decomposition and the numerical instability at the Brewster angle. At the same time, it ensures the rapid solution of the 3DPE on the flat ground, and realizes the efficient prediction of the low-frequency ground wave propagation characteristics of the hybrid propagation path in three-dimensional space.

Description

Technical Field

[0001] The present invention belongs to the technical field of radio wave propagation, and in particular relates to a method and system for predicting low-frequency ground wave propagation characteristics of a partitioned hybrid path. Background Art

[0002] Currently, accurate prediction of propagation delay has become a key factor limiting the accuracy of low-frequency radio navigation and timing systems. As the accuracy requirements for ground-based navigation and timing systems continue to increase, methods for predicting low-frequency ground wave propagation characteristics are expanding into three dimensions. The three-dimensional parabolic equation (3DPE) method, originally used to study underwater acoustic wave propagation, has recently been widely studied and applied in the field of radio wave propagation. Compared to the two-dimensional parabolic equation (2DPE) method, the 3DPE method can reflect the influence of lateral medium parameters on the lateral propagation characteristics of low-frequency ground waves during forward propagation. Furthermore, because the 3DPE method can be solved using the Split-Step Fourier Transform (SSFT) algorithm, it offers advantages when predicting low-frequency ground wave propagation characteristics over large areas.

[0003] However, the traditional SSFT algorithm based on field parity decomposition has the problem of unstable field values at the Brewster angle. Due to the influence of the Brewster angle, the reflection coefficient of the TM wave, i.e. the transverse magnetic wave, will produce singular points. This will have a significant impact on the prediction of low-frequency ground wave propagation characteristics, causing sudden changes in field values and divergence in time delays, which in turn leads to inaccurate prediction results of low-frequency ground wave propagation characteristics.

[0004] The current SSFT algorithm for solving 3DPE is limited by its algorithm stability, and it is difficult to achieve efficient and stable prediction of the propagation characteristics of low-frequency ground waves in wide-area partitioned mixed paths. Especially in large-scale computing areas and long-term simulation scenarios, the demand for computing resources increases significantly, making it difficult to meet the efficiency requirements of actual engineering applications.

[0005] Therefore, studying a method that can efficiently and stably predict the propagation characteristics of low-frequency ground waves in partitioned mixed paths has become a technical problem that needs to be solved urgently. Summary of the Invention

[0006] The purpose of the present invention is to propose a method for predicting low-frequency ground wave propagation characteristics of partitioned hybrid paths. The method is suitable for predicting low-frequency ground wave propagation characteristics. It uses the SSFT algorithm combining FFT and DMFT to solve 3DPE. While accelerating the solution speed of 3DPE, it can ensure the accuracy in solving low-frequency ground wave propagation problems.

[0007] In order to achieve the above-mentioned purpose, the present invention adopts the following technical solutions:

[0008] A method for predicting low-frequency ground wave propagation characteristics of a partitioned mixed path includes the following steps:

[0009] Step 1. Input the model file. The content of the input model file includes the grid parameters of the calculation area, the excitation source parameters, and the electrical parameters of the radio wave propagation path;

[0010] Step 2. Use the flat ground formula to calculate the propagation path of the radio wave from the excitation source Magnetic field at , through the magnetic field Initial field distribution for solving three-dimensional parabolic equations ;

[0011] Step 3. Use the discrete hybrid Fourier transform and fast Fourier transform to solve the three-dimensional parabolic equation step by step and obtain the field distribution results in the entire calculation area.

[0012] Step 4. Use the field distribution results in the entire calculation area to calculate the magnetic field strength of the low-frequency ground wave propagating on the partitioned mixed path And the secondary delay generated .

[0013] In addition, based on the method for predicting the low-frequency ground wave propagation characteristics of a partitioned hybrid path, the present invention also proposes a corresponding system for predicting the low-frequency ground wave propagation characteristics of a partitioned hybrid path, the technical solution of which is as follows:

[0014] A system for predicting low-frequency ground wave propagation characteristics of partitioned mixed paths, comprising:

[0015] The model parameter initialization module is used to input the model file. The content of the input model file includes the grid parameters of the calculation area, the excitation source parameters, and the electrical parameters of the radio wave propagation path;

[0016] The initial field distribution solution module is used to calculate the initial field distribution of the excitation source in the radio wave propagation path using the flat ground formula. Magnetic field at , through the magnetic field Initial field distribution for solving three-dimensional parabolic equations ;

[0017] The parabolic equation solving module is used to solve the three-dimensional parabolic equation step by step using a discrete hybrid Fourier transform and a fast Fourier transform algorithm to obtain the field distribution results in the entire calculation area;

[0018] And the propagation characteristics prediction module is used to use the field distribution results in the entire calculation area to calculate the magnetic field intensity of low-frequency ground waves propagating on the partitioned mixed path And the secondary delay generated .

[0019] In addition, based on the above-mentioned method for predicting low-frequency ground wave propagation characteristics of partitioned mixed paths, the present invention also proposes a computer device, which includes a memory and one or more processors;

[0020] The memory stores executable codes, and when the processor executes the executable codes, it is used to implement the steps of the above-mentioned method for predicting low-frequency ground wave propagation characteristics of partitioned hybrid paths.

[0021] In addition, based on the above-mentioned method for predicting the low-frequency ground wave propagation characteristics of partitioned hybrid paths, the present invention also proposes a computer-readable storage medium on which a program is stored; when the program is executed by a processor, it is used to implement the steps of the above-mentioned method for predicting the low-frequency ground wave propagation characteristics of partitioned hybrid paths.

[0022] The present invention has the following advantages:

[0023] As described above, the present invention describes a method for predicting the propagation characteristics of low-frequency ground waves in partitioned hybrid paths. The method is applicable to low-frequency ground waves and can quickly solve 3DPE. The method of the present invention uses an SSFT algorithm that combines DMFT and FFT to speed up the solution of 3DPE. By converting the reflection coefficient with singular points into impedance coefficients and performing directional processing on the double-integral SSFT solution, it not only improves the stability of the SSFT algorithm solution, but also realizes efficient and stable prediction of the propagation characteristics of low-frequency ground waves in wide-area partitioned hybrid paths. The method of the present invention solves the problem that the lateral wave propagation of low-frequency ground waves is affected by the fact that 2DPE does not take into account the irregular boundaries between hybrid paths, and at the same time overcomes the singularity caused by the reflection coefficient of the SSFT algorithm based on field parity decomposition and the numerical instability at the Brewster angle. Moreover, the method of the present invention has more advantages in predicting the propagation characteristics of low-frequency ground waves in large-scale complex terrain scenes and is suitable for promotion in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 Flowchart of the method for predicting low-frequency ground wave propagation characteristics of partitioned hybrid paths in an embodiment of the present invention.

[0025] Figure 2 Schematic diagram of the principle of the method for predicting low-frequency ground wave propagation characteristics of a partitioned hybrid path in an embodiment of the present invention Figure 1 .

[0026] Figure 3Schematic diagram of the principle of the method for predicting low-frequency ground wave propagation characteristics of a partitioned hybrid path in an embodiment of the present invention Figure 2 .

[0027] Figure 4 In order to use the method of the present invention, the 3D-FDTD method and the analytical method flat ground formula in azimuth The calculated magnetic field strength H when the y Schematic diagram of the results.

[0028] Figure 5 In order to use the method of the present invention, the 3D-FDTD method and the analytical method flat ground formula in azimuth The second time delay t calculated when the value is 3° w Schematic diagram of the results.

[0029] Figure 6 Schematic diagram of the sea-land hybrid propagation path in an embodiment of the present invention.

[0030] Figure 7 To predict the low-frequency ground wave magnetic field intensity H on the sea-land mixed path using the method of the present invention y Schematic diagram of the results.

[0031] Figure 8 To predict the secondary delay t of low-frequency ground waves on a sea-land mixed path using the method of the present invention w Schematic diagram of the results. DETAILED DESCRIPTION

[0032] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0033] The present invention provides a partitioned hybrid path low-frequency ground wave propagation characteristics prediction method, which is applicable to low-frequency ground waves and adopts an efficient SSFT algorithm that can quickly solve 3DPE. By combining Fast Fourier Transform (FFT) and Discrete Mixed Fourier Transform (DMFT), the speed of solving 3DPE is accelerated, while the correctness of solving the low-frequency ground wave propagation problem is guaranteed, thereby enriching the research field of low-frequency ground wave prediction problems in complex terrain environments.

[0034] The method of the present invention solves the problem that the lateral propagation of low-frequency ground waves is affected by the 2DPE method because the irregular intersection between hybrid paths is not considered. At the same time, it overcomes the singularity caused by the reflection coefficient of the SSFT algorithm based on field parity decomposition and the numerical instability at the Brewster angle. The overall process is as follows:

[0035] First, the model parameters are input; then, the initial field distribution of the parabola equation at the initial position is obtained using the flat ground formula; then, the SSFT algorithm combining DMFT and FFT is used to solve the 3DPE; finally, the field results in the entire calculation area are used to calculate the magnetic field strength of the radio wave propagation. and quadratic delay .

[0036] Based on the above invention concept, the prediction method of low-frequency ground wave propagation characteristics of the partitioned mixed path proposed by the present invention is described in detail below with reference to the accompanying drawings. Figure 1 As shown, the method of the present invention specifically comprises the following steps:

[0037] Step 1. Input the model file. The content of the input model file includes the grid parameters of the calculation area, the excitation source parameters, and the electrical parameters of the radio wave propagation path.

[0038] In this embodiment, the parameters input into the model and initialized include the grid parameters of the simulation area, i.e. the entire calculation area, the excitation source parameters, the electrical parameters of the simulation path, i.e. the radio wave propagation path, the absorption boundary and the lower boundary parameters.

[0039] like Figure 2 As shown, in the three-dimensional rectangular coordinate system, the calculation area size is defined as The calculation area is divided into N in the horizontal x, vertical y and height z directions respectively. x 、N y and N z grids, 、 and is the spatial grid step size. Figure 2 In the equation, O represents the origin of the coordinate system of the calculation area. To simplify the formula, we introduce the substitution variable Representing the maximum distance in each direction, we get:

[0040] (1)

[0041] in, .

[0042] The excitation source is a vertical electric dipole, and the current I and charge spacing dl of the vertical magnetic dipole are preset.

[0043] In this embodiment, the partitioned hybrid path of radio wave propagation is a land-sea hybrid path. The flat ground path is used to verify the correctness of this method. The electrical parameters of the flat ground and land-sea hybrid paths include the dielectric constant and conductivity .

[0044] Step 2. Use the flat ground formula to calculate the propagation path of the radio wave from the excitation source Magnetic field at , through the magnetic field Initial field distribution for solving three-dimensional parabolic equations .

[0045] For the propagation problem of low-frequency ground waves, the flat ground formula in the analytical solution is selected as the initial field of 3DPE, and the preset initial distance ,at this time Ground wave magnetic field component Expressed as:

[0046] (2)

[0047] Among them, the vertical electric dipole lie in Axle off the ground At the height of , i represents the imaginary unit, is the propagation constant in vacuum, is the ground wave number, r1 represents the distance from the source point where the vertical electric dipole is placed in the calculation area to the initial field position of the observation The straight-line distance from the observation point at , r2 represents the straight-line distance from the mirror point of the source point to the observation point, and P2 is the intermediate parameter.

[0048] (3)

[0049] (4)

[0050] (5)

[0051] For the preset initial distance According to formula (2), the initial field of low-frequency ground wave is obtained for:

[0052] (6)

[0053] The initial state of the field is set to establish a complete parameterized calculation framework for high-precision numerical simulation of field propagation characteristics in three-dimensional terrain.

[0054] Step 3. Use the discrete hybrid Fourier transform and fast Fourier transform to solve the three-dimensional parabolic equation step by step and obtain the field distribution results in the entire calculation area.

[0055] The computational domain of the three-dimensional parabolic equation 3DPE consists of the upper and lower boundaries and the initial boundary.

[0056] The upper boundary is the absorbing boundary, which is set as the window functions W(y) and W(z) added in the y and z directions:

[0057] (7)

[0058] (8)

[0059] in, To calculate the maximum distance of the area along the y direction, To calculate the maximum height of the region along the z direction, starting from the initial distance, the field distribution calculated by the parabolic equation PE is multiplied by W(y) and W(z) at each step.

[0060] The lower boundary condition is the surface boundary, and the impedance boundary condition is adopted, that is:

[0061] (9)

[0062] in, is the impedance characteristic parameter on the boundary surface. express The field distribution at is the impedance characteristic parameter on the boundary surface.

[0063] The initial boundary is the initial field distribution, that is, the initial field distribution of 3DPE obtained by formula (2) and formula (6) in step 2 .

[0064] like Figure 3 As shown, the method of the present invention calculates the field on each stepping plane of the calculation area. First, the FFT method is used to accelerate the calculation of the outer integral in the y direction. Then, the inner integral in the z direction is solved using the DMFT method that incorporates the transform domain flat ground impedance boundary condition. When solving the inverse transform, it is necessary to first calculate the inverse discrete Fourier transform (IDMFT) in the z direction, and then calculate the inverse fast Fourier transform (IFFT) in the y direction.

[0065] Step 3.1. Initial field distribution Written in a discretized form :

[0066] Preset initial distance , the initial field Written in a discretized form .

[0067] in, , , 、 Represents each grid point along the y and z directions respectively.

[0068] Step 3.2. First find the initial field along the y direction The FFT of .

[0069] (10)

[0070] in, express The field distribution obtained by fast Fourier transform along the y direction is, represents the discrete wave number in the y direction.

[0071] Step 3.3. Calculate the field along the z direction again The DMFT of , without considering the refractive index term, Multiply it by its diffraction index along the z direction .

[0072] First, the method and steps for implementing DMFT are as follows: the calculation area is divided into N z grid, combined with the Nyquist Criterion, the specific expression of DMFT is:

[0073] (11)

[0074] in, Indicates that when calculating the sum, and Multiply both of these by , express Field distribution obtained by discrete mixed Fourier transform along the z direction, j = 0, 1, ..., N z , represents the discrete wave number in the z direction.

[0075] Then, ignoring the refractive index term, Multiply by the diffraction index in the z direction ,get:

[0076] (12)

[0077] in, express Multiply by the diffraction index in the z direction The obtained field distribution is represents the wave number in the x direction.

[0078] Step 3.4. Playing the field Inverse discrete Fourier transform IDMFT along the z direction to obtain the field distribution .

[0079] Solving the inverse transform of DMFT requires deriving some formulas based on the impedance boundary conditions. The specific steps are:

[0080] Convert the impedance boundary condition of formula (9) into a differential equation:

[0081] (13)

[0082] in, express The field value distribution at express The field value at the next grid point, express The field value at the previous grid point.

[0083] The characteristic equation of formula (13) is:

[0084] (14)

[0085] in, represents the eigenvalue of the characteristic equation, and the solution is:

[0086] , To ensure the stability of the final solution, it is necessary to 、 Select the one with a modulus less than 1 as the required ;set up:

[0087] (15)

[0088] in, and Calculate coefficients for intermediate variables, .

[0089] Zechang The inverse discrete Fourier transform along the z direction is defined as:

[0090] (16)

[0091] in, represents the number of sampling points in the inverse discrete Fourier transform, express The discrete Fourier transform form of .

[0092] To further simplify the calculation of sine and cosine in formula (16), the differential form of the impedance boundary condition is used as an auxiliary function :

[0093] (17)

[0094] Define Field The discrete sine transform (DST) and its inverse transform (IDST) along the z direction are:

[0095] (18)

[0096] Performing DST calculation on formula (17), we can find that ,Right now:

[0097] (19)

[0098] Among them, the symbol Represents discrete mixture Fourier transform DMFT, the above formula shows Can be The IDST solution is obtained.

[0099] According to the auxiliary function , we can find the appearance by formula (17) ,Right now:

[0100] (20)

[0101] in, is the special solution of formula (20), 、 is the coefficient.

[0102] Solved by backward recursive algorithm, since If formula (16) is satisfied, then The difference equation is decomposed into:

[0103] (twenty one)

[0104] Formula (21) has ; If:

[0105] (twenty two)

[0106] in, Indicates in the z direction The particular solution value at the grid point; then formula (21) becomes:

[0107] (twenty three)

[0108] According to formula (22) and formula (23), let 、 , That is , represents the value at the initial grid point in the z direction, That is , Indicates in the z direction The specific solution value at the grid point is obtained by the backward recursive algorithm .

[0109] and The calculation steps are as follows:

[0110] (twenty four)

[0111] (25)

[0112] For both ends of formula (20), and The formal summation calculation yields:

[0113] (26)

[0114] In the above formula and Also perform step calculations, their initial values and Calculated by formula (14), the step value and Then:

[0115] (27)

[0116] (28)

[0117] Using formula (20) to formula (28) to calculate the field By finding the inverse DMFT along the z direction, we can get the corresponding field distribution .

[0118] Step 3.5. Perform inverse fast Fourier transform to obtain the field distribution .

[0119] Step 3.6. Finally, consider the refractive index term. Use Multiply , thus the field distribution on the next step surface is obtained from the initial field calculation.

[0120] Step 3.7. Repeat steps 3.1 to 3.6 until the field distribution in the entire calculation area is obtained.

[0121] On each stepping plane, the present invention first uses FFT to solve the outward integral in the y direction and DMFT to solve the inward integral in the z direction, and then performs calculations on the next stepping plane. This accelerates the solution of the field distribution and improves the stability and computational efficiency of the SSFT algorithm compared to the SSFT algorithm that uses odd-even field decomposition.

[0122] Step 4. Use the field distribution results in the entire calculation area to calculate the magnetic field strength of the low-frequency ground wave propagating on the partitioned mixed path And the secondary delay generated .

[0123] Step 4.1. The field at each step calculated in step 3 Substitute into the following formula to find all magnetic fields in the calculation area :

[0124] (29)

[0125] Step 4.2. Calculate the magnetic field at all locations in the calculation area using step 4.1 , then the magnetic field at each position Extract the real and imaginary parts and calculate the phase:

[0126] (30)

[0127] in, represents the operation of extracting the real part, Indicates the operation of extracting the imaginary part; phase Characterizes the accumulated phase delay of electromagnetic waves in the propagation path.

[0128] When the radio wave propagation path is set as a partitioned hybrid path, the phase φ of the low-frequency ground wave propagating on the partitioned hybrid path is obtained by formula (30): ac When the radio wave propagation path is set to a good conductor path, the phase φ of the low-frequency ground wave propagating on the good conductor path is obtained by formula (30): re .

[0129] Substituting the phase difference between the two paths into the formula gives the quadratic delay. Calculate the quadratic delay The formula is as follows:

[0130] t w =φ ac－ φ re .

[0131] Among them, φ ac is the phase of the electromagnetic field when it propagates on the actual hybrid path, φ reis the phase of the electromagnetic field when it propagates on a good conductor path.

[0132] In addition, in order to verify the effectiveness of the method proposed in the present invention, the following specific experiments are given:

[0133] Experiment 1: The azimuth angle was calculated by using the DMFT+FFT method of the present invention, the three-dimensional finite-difference time-domain (3D-FDTD), and the analytical method of the flat ground formula. The calculated magnetic field strength H when the y and the secondary delay t w results.

[0134] In this experiment, the total length of the radio wave propagation path is set to 100 km. The operating frequency of the transmitter is 100 kHz, and the atmospheric refractive index is set to , the initial field is calculated by the flat ground formula and the position is km. For the 3D-FDTD method, the calculation area is , , , the grid size is defined as = = =18m, time step According to the CFL stability condition, it is taken as 20ns. For the 3DPE method, the calculation area is , , , the grid step size is m, m. The ground electrical parameters are , S / m.

[0135] Figure 4 and Figure 5 The azimuths are given When the magnetic field intensity H is calculated by the method of the present invention, the three-dimensional time-domain finite difference method and the analytical method flat ground formula, y and the secondary delay t w The result of Figure 4 and Figure 5 It can be seen from the results that the prediction method of the present invention is in good agreement, which proves the applicability and correctness of the method of the present invention in the low-frequency ground wave propagation problem.

[0136] Experiment 2: Prediction results of magnetic field strength and secondary time delay for low-frequency ground wave propagation over a mixed land-sea path.

[0137] In this experiment, the initial field of the flat ground 3DPE is calculated by the flat ground formula, and the initial field position is located at km. Assuming the total length of the radio wave propagation path is 100 km, the calculation area size of 3DPE is { , , }, the grid is m, m. Figure 6 A schematic diagram of the sea-land mixed propagation path is given. The sea-land boundary shows an irregular distribution. The yellow part is land. The electric constant of the land area is , the conductivity of the land area is S / m; the blue part is seawater, and the electrical constant of the seawater area is The conductivity of the seawater area is S / m.

[0138] Figure 7 and Figure 8 This is the effect of the sea-land mixed propagation path on the propagation characteristics of low-frequency ground waves. It can be seen that the magnetic field intensity H of the low-frequency ground wave y The change of the secondary delay t w Under the mixed sea-land path, the path is affected by the irregular boundary of the mixed path. Where the boundary changes drastically, the maximum change is about 300ns.

[0139] The method of the present invention overcomes the error problem caused by the traditional two-dimensional modeling method assuming that the mixed path is uniformly distributed at the intersection when predicting low-frequency ground wave propagation. Compared with the existing odd-even decomposition SSFT algorithm for solving 3DPE, the method of the present invention solves the problem of singular points in the reflection coefficient of the TM wave caused by the influence of the Brewster angle. It uses a combination of FFT and DMFT to speed up the solution of 3DPE and improve the calculation efficiency. At the same time, it can ensure the correctness when solving the low-frequency ground wave propagation problem, and realize the efficient prediction of mixed propagation paths in three-dimensional space.

[0140] The traditional SSFT algorithm based on field parity decomposition suffers from unstable field values at the Brewster angle. The influence of the Brewster angle can cause singular points in the reflection coefficient of the TM wave, which has a significant impact on the prediction of low-frequency ground wave propagation. In contrast, the SSFT algorithm, which combines discrete hybrid Fourier transform with fast Fourier transform, converts the reflection coefficient with singular points into impedance coefficients and performs directional processing on the double-integrated SSFT solution. This not only improves the stability of the SSFT algorithm solution and achieves efficient and stable prediction of low-frequency ground wave propagation characteristics in wide-area partitioned hybrid paths, but also improves the computational efficiency of the SSFT algorithm.

[0141] The method of the present invention solves the problem that the lateral wave propagation of low-frequency ground waves is affected by the two-dimensional parabolic equation method because the irregular intersection between the mixed paths is not taken into account. It overcomes the singularity and numerical instability problems at the Brewster angle caused by the influence of the reflection coefficient in the SSFT algorithm based on field parity decomposition. At the same time, it ensures the rapid solution of 3DPE on flat ground and realizes the efficient prediction of mixed propagation paths in three-dimensional space.

[0142] Example 2

[0143] This embodiment 2 describes a system for predicting low-frequency ground wave propagation characteristics of a partitioned hybrid path. This system is based on the same inventive concept as the method for predicting low-frequency ground wave propagation characteristics of a partitioned hybrid path in embodiment 1.

[0144] Specifically, the partitioned hybrid path low-frequency ground wave propagation characteristics prediction system includes the following modules:

[0145] The model parameter initialization module is used to input the model file. The content of the input model file includes the grid parameters of the calculation area, the excitation source parameters, and the electrical parameters of the radio wave propagation path.

[0146] The initial field distribution solution module is used to calculate the initial field distribution of the excitation source in the radio wave propagation path using the flat ground formula. Magnetic field at , through the magnetic field Initial field distribution for solving three-dimensional parabolic equations .

[0147] The parabolic equation solving module is used to solve the three-dimensional parabolic equation step by step using a step-by-step Fourier transform algorithm that combines discrete mixed Fourier transform and fast Fourier transform to obtain the field distribution results in the entire calculation area.

[0148] And the propagation characteristics prediction module is used to use the field distribution results in the entire calculation area to calculate the magnetic field strength of low-frequency ground waves propagating on the partitioned mixed path And the secondary delay generated .

[0149] Example 3

[0150] This embodiment 3 describes a computer device, which includes a memory and one or more processors.

[0151] The memory stores executable codes, which, when executed by the processor, are used to implement the steps of the method for predicting low-frequency ground wave propagation characteristics of partitioned hybrid paths in the above-mentioned embodiment 1.

[0152] In this embodiment, the computer device is any device or apparatus with data processing capability, which will not be described in detail here.

[0153] Example 4

[0154] This embodiment 4 describes a computer-readable storage medium having a program stored thereon. When the program is executed by a processor, the program is used to perform the steps of a method for predicting low-frequency ground wave propagation characteristics of a partitioned hybrid path.

[0155] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc. equipped on the device.

[0156] Of course, the above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above-mentioned embodiments. It should be noted that all equivalent substitutions and obvious deformation forms made by any technician familiar with this field under the guidance of this specification fall within the substantive scope of this specification and should be protected by the present invention.

Claims

1. A method for predicting low-frequency ground wave propagation characteristics of a partitioned mixed path, characterized in that: The steps include: Step 1. Input the model file. The content of the input model file includes the grid parameters of the calculation area, the excitation source parameters, and the electrical parameters of the radio wave propagation path; Step 2. Use the flat ground formula to calculate the magnetic field H at the excitation source at x = x0 on the radio wave propagation path. y (x0,y,z), through the magnetic field H y (x0,y,z) solves the initial field distribution u(x0,y,z) of the three-dimensional parabolic equation; Step 3. Use the discrete hybrid Fourier transform and fast Fourier transform combined step-by-step Fourier transform algorithm to solve the three-dimensional parabolic equation step by step to obtain the field distribution results in the entire calculation area; Step 4. Use the field distribution results in the entire calculation area to calculate the magnetic field intensity H of the low-frequency ground wave propagating on the partitioned mixed path y And the resulting secondary delay t w ; The step 3 is specifically as follows: Step 3.

1. Write the initial field distribution u(x0, y, z) into a discretized representation u(x0, lΔy, mΔz); Where l = 1, 2, ..., N y ,m=0,1,...,N z , lΔy, mΔz represent each grid point along the y and z directions respectively; in the three-dimensional rectangular coordinate system (x, y, z), N x is the number of grids in the x-direction of the horizontal coordinate, N y is the number of grids in the y-direction of the longitudinal coordinate, N z is the number of grids in the height coordinate z direction; Δx, Δy and Δz are the spatial grid steps; Step 3.

2. Calculate the fast Fourier transform (FFT) of the initial field distribution u(x0, lΔy, mΔz) along the y direction and obtain the field distribution Where Δk y represents the discrete wave number in the y direction, i represents the imaginary unit; Step 3.

3. Calculate the field distribution along the z direction The discrete mixture Fourier transform DMFT, the calculation area is divided into N in the height z direction z grids, combined with the Nyquist criterion, we can get the field distribution The expression is: Where ∑' means multiplying both m=0 and m=N by 1 / 2 when calculating the sum, j=0,1,…,N z , Δk z represents the discrete wave number in the z direction; Ignoring the refractive index term, Multiply by the diffraction index in the z direction get: Among them, k x represents the wave number in the x direction; Step 3.

4. Field distribution U(x0+Δx,lΔk y ,jΔk z ) Take the inverse discrete Fourier transform IDMFT along the z direction to get the field distribution Step 3.

5. Perform inverse fast Fourier transform IFFT along the y direction to obtain the field distribution u(x0+Δx,lΔy,mΔz); Step 3.

6. Consider the refractive index term and use Multiply by u(x0+Δx,lΔy,mΔz) to get the field distribution on the next step; Step 3.

7. Repeat steps 3.1 to 3.6 until the field distribution results in the entire calculation area are obtained.

2. The method for predicting low-frequency ground wave propagation characteristics of a partitioned hybrid path according to claim 1, characterized in that: The step 1 is specifically as follows: In the three-dimensional rectangular coordinate system (x, y, z), the calculation area size is defined as N x ×N y ×N z ; Introducing the alternative variable ξ to represent the maximum distance in each direction, we get: ξ=N ξ Right (1) Where ξ=x,y,z; The excitation source is a vertical electric dipole, and the current I and charge spacing dl of the vertical magnetic dipole are preset; The electrical parameters of the radio wave propagation path, i.e., the flat ground and the mixed land-sea path, include the dielectric constant ε r and conductivity σ.

3. The method for predicting low-frequency ground wave propagation characteristics of partitioned hybrid paths according to claim 2, characterized in that: The step 2 is specifically as follows: The flat ground formula in the analytical solution is selected as the initial field of the three-dimensional parabolic equation 3DPE. The preset initial distance is x = x0. The ground wave magnetic field component H at x = x0 is y (x0,y,z) is expressed as: where the vertical electric dipole is located at a height h above the ground on the z-axis, k0 is the propagation constant in vacuum, and k g is the ground wave number, r1 represents the straight-line distance from the source point where the vertical electric dipole is placed in the calculation area to the observation point at the initial field position x0, r2 represents the straight-line distance from the mirror point of the source point to the observation point, and P2 is an intermediate parameter; For the initial distance x = x0, the initial field distribution u(x0, y, z) of the low-frequency ground wave is obtained according to formula (2):

4. The method for predicting low-frequency ground wave propagation characteristics of partitioned hybrid paths according to claim 3, characterized in that: In step 3, the calculation area of the three-dimensional parabolic equation 3DPE consists of the upper boundary, the lower boundary and the initial boundary; The upper boundary is the absorbing boundary, which is set as the window functions W(y) and W(z) added in the y and z directions: Among them, y max To calculate the maximum distance of the area along the y direction, z max is the maximum height of the calculation area along the z direction; Starting from the initial distance, the field distribution calculated by the parabolic equation PE is multiplied by W(y) and W(z) at each step; The lower boundary condition is the surface boundary, and the impedance boundary condition is adopted, that is: Where u(x,y,z) represents the field distribution at (x,y,z), and α is the impedance characteristic parameter on the boundary surface; The initial boundary is the initial field distribution, that is, the initial field distribution u(x0,y,z) of 3DPE obtained in step 2 by formula (2) and formula (6).

5. The method for predicting low-frequency ground wave propagation characteristics of partitioned hybrid paths according to claim 4, characterized in that: The step 3.4 is specifically as follows: Convert the impedance boundary condition of formula (9) into a differential equation: Among them, u(x,y,mΔz) represents the field value distribution at (x,y,mΔz), u(x,y,(m+1)Δz) represents the field value of the grid point next to u(x,y,mΔz), and u(x,y,(m-1)Δz) represents the field value of the grid point previous to u(x,y,mΔz); The characteristic equation of formula (13) is: l 2 +2laΔz-1=0 (14) Where λ represents the eigenvalue of the characteristic equation, and the solution is: To ensure the stability of the final solution, select an item with a modulus less than 1 from λ1 and λ2 as λ; let: Among them, C1 and C2 are the calculation coefficients of intermediate variables, Then the field distribution U(x0+Δx,lΔk y ,jΔk z ) The inverse discrete Fourier transform along the z direction is defined as: in, Represents the discrete Fourier transform form of u(x,y,mΔz); The differential form of the impedance boundary condition is used as the auxiliary function g(x,y,mΔz): The discrete sine transform DST and inverse transform IDST of the field u(x,y,z) along the z direction are defined as follows: Where DST[u] represents the field distribution obtained by discrete sine transform of u(x,y,z) along the z direction; Perform DST calculation on formula (17) and get Right now: in, Denotes the discrete mixed Fourier transform, g(x,y,mΔz) is given by The IDST solution of According to the auxiliary function g(x,y,mΔz), the field distribution u(x,y,mΔz) is obtained by formula (17): Among them, u p (x, y, mΔz) is the particular solution of formula (20), B1 and B2 are coefficients; u p (x,y,mΔz) is solved by the backward recursive algorithm, since u p (x, y, mΔz) satisfies formula (16), then with respect to u p The difference equation of (x,y,mΔz) is decomposed into: In formula (21), λ-1 / λ=-2αΔz; if we set: Among them, u p (x,y,(m+1)Δz) represents the particular solution value at the m+1 grid point in the z direction; then formula (21) becomes: s(x,y,mΔz)-λ·s(x,y,(m-1)Δz)=2Δz·g(x,y,mΔz) (23) According to formula (22) and formula (23), let s(0) = 0, u p (N z )=0, s(0) is s(x,y,0Δz), s(x,y,0Δz) represents the particular solution value at the initial grid point in the z direction, u p (N z ) is u p (x,y,N z Δz),u p (x,y,N z Δz) represents the z direction N z The special solution value at the grid point is obtained by the backward recursive algorithm. p (x,y,mΔz); The calculation steps for B1 and B2 are: For both ends of formula (20), and The formal summation calculation yields: The initial values of C1 and C2, C1(x) and C2(x), are calculated by formula (15), and the step values, C1(x+Δx) and C2(x+Δx), are: Using formula (20) to formula (28) to calculate the field distribution U(x0+Δx,lΔk y ,jΔk z ) Inverse discrete Fourier transform along the z direction to obtain the field distribution 6. The method for predicting low-frequency ground wave propagation characteristics of partitioned hybrid paths according to claim 5, characterized in that: The step 4 is specifically as follows: Substitute the field distribution u(x, y, z) at each step calculated in step 3 into formula (29) to obtain the total magnetic field H in the calculation area. y (x,y,z): For each position in the calculation area, the magnetic field H y (x,y,z) extract the real and imaginary parts and calculate the phase Among them, Re(·) represents the operation of extracting the real part, and Im(·) represents the operation of extracting the imaginary part; Represents the cumulative phase delay of the electromagnetic wave in the propagation path; When the radio wave propagation path is set as a partitioned hybrid path, the phase of the low-frequency ground wave propagating on the partitioned hybrid path is obtained by formula (30): When the radio wave propagation path is set as a good conductor path, the phase of the low-frequency ground wave propagating on the good conductor path is obtained by formula (30): Calculate the secondary delay t caused by low-frequency ground waves propagating on the partitioned mixed path w The formula is:

7. A system for predicting low-frequency ground wave propagation characteristics of a partitioned hybrid path for implementing the method for predicting low-frequency ground wave propagation characteristics of a partitioned hybrid path as claimed in claim 1, characterized in that: The partitioned hybrid path low-frequency ground wave propagation characteristics prediction system includes: The model parameter initialization module is used to input the model file. The content of the input model file includes the grid parameters of the calculation area, the excitation source parameters, and the electrical parameters of the radio wave propagation path; The initial field distribution solution module is used to calculate the magnetic field H at the position x=x0 of the excitation source on the radio wave propagation path using the flat ground formula. y (x0,y,z), through the magnetic field H y (x0,y,z) solves the initial field distribution u(x0,y,z) of the three-dimensional parabolic equation; The parabolic equation solving module is used to solve the three-dimensional parabolic equation step by step using a discrete hybrid Fourier transform and a fast Fourier transform algorithm to obtain the field distribution results in the entire calculation area; And the propagation characteristics prediction module is used to use the field distribution results in the entire calculation area to calculate the magnetic field intensity H of the low-frequency ground wave propagating on the partitioned mixed path y And the resulting secondary delay t w .

8. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that: When the processor executes the executable code, the steps of the method for predicting low-frequency ground wave propagation characteristics of partitioned hybrid paths according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method for predicting low-frequency ground wave propagation characteristics of a partitioned hybrid path as claimed in any one of claims 1 to 6 are implemented.

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