Day and night transition area electron density inversion method

Abstract

The invention discloses a day and night transition area electron density inversion method, which comprises the following steps: firstly, starting from extracting a solar zenith angle of a VLF wave propagation path at different moments, providing a subsection correction electron density model suitable for a low ionosphere, and introducing the correction electron density model changing along with the zenith angle into a frequency domain finite element method; a ground-ionosphere waveguide VLF wave amplitude and phase propagation data set is constructed, VLF wave simulation and test data are introduced into an artificial intelligence model, and inversion of corrected electron density parameters is realized. According to the method, the zenith angle and the corrected electron density model are introduced, and VLF wave propagation numerical simulation and experimental testing are combined, so that the constructed artificial intelligence model can quickly and accurately predict the electron density of the day and night transition region of the ionosphere D region.

Description

Technical Field

[0001] The invention belongs to the field of electronic information technology, and particularly relates to an electron density inversion method for a day-night transition zone. Background Art

[0002] The development of polar shipping routes will have a profound impact on global geopolitics. Satellite communications and navigation in the polar regions face the challenge of low satellite visibility angles. The positioning error of ships' inertial navigation systems increases over time, making a single mode unable to meet communication and navigation needs. Very Low Frequency (VLF) electromagnetic waves, operating at 3-30 kHz, offer wide coverage, all-day operation, and strong water penetration. Developing technologies to improve the predictive efficiency of VLF communication and navigation systems can effectively address the problem of other communication and navigation systems failing to operate properly in polar environments, thereby enhancing the competitiveness of my country's polar strategy.

[0003] In addition to being limited by the simulation accuracy of analytical and numerical methods for Earth-ionosphere waveguides, the accuracy of very low frequency (VLF) electromagnetic wave propagation simulations depends primarily on the accuracy of the temporally and spatially varying lower ionospheric electron density model. The International Reference Ionosphere (IRI) electron density model, the Chinese Reference Ionosphere Model, and exponential models are all unable to accurately predict the field strength and phase of VLF waves during the diurnal transition period. The paper "Finite Element Method Study of VLF Wave Propagation Characteristics in a Fine Earth-Ionosphere Waveguide" proposes an IRI electron density model modified for solar zenith angle at different altitudes. However, the VLF wave propagation results exhibit symmetry during the diurnal transition period at sunrise and sunset, which is inconsistent with the test results. To date, no reports have been published on modified electron density models that account for sunrise and sunset effects and contain both straight lines and Langevin functions at different solar zenith angles. Summary of the Invention

[0004] In response to the above-mentioned deficiencies in the prior art, the electron density inversion method for the day-night transition zone provided by the present invention solves the problems in the prior art of inaccurate low ionosphere electron density model during the day-night transition period and low efficiency in extracting low ionosphere electron density parameters.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: a method for inverting the electron density in the day-night transition zone, comprising the following steps:

[0006] S1, extracting the solar zenith angle of any transmission path of very low frequency electromagnetic waves;

[0007] S2. Based on the IRI model, the electron density is fitted with the variation of the solar zenith angle and the altitude above the ground, and a modified electron density model containing a straight line and a Langevin function is obtained, which is suitable for the lower ionosphere to characterize the variation of the electron density with time and space;

[0008] S3. Introducing Universal Time, the solar zenith angle, and the modified electron density model into the Earth-ionosphere waveguide model constructed based on the FEM method, numerical simulations were used to generate very low frequency electromagnetic wave propagation datasets under different spatiotemporal distributions of electron density.

[0009] S4. Using the very low frequency electromagnetic wave propagation dataset to train the artificial intelligence model, an electron density inversion model is obtained that reflects the mapping relationship between the parameters in the modified electron density model and the very low frequency electromagnetic wave propagation;

[0010] S5. Input the test amplitude and phase of the very low frequency electromagnetic waves in the day-night transition zone that change with the universal time into the electron density inversion model, and invert the spatiotemporal distribution of the electron density in the ionosphere D region along the very low frequency electromagnetic wave propagation path.

[0011] Furthermore, in step S1, the solar zenith angle χ at any position is:

[0012] χ=90°-H

[0013] Where H represents the solar altitude angle, which satisfies:

[0014] sinH=cosα m cosδcosΩ+sinα m sinδ

[0015] δ=0.3723+23.2567sinθ+0.1149sin2θ-0.1712sin3θ-0.758cosθ+0.3656cos2θ+0.0201cos3θ

[0016] Ω=15[S+F / 60+(λ m -λ s ) / 15+E q -12]

[0017] E q =(0.0028-1.9857sinθ+9.9059sin2θ-7.0924cosθ-0.6882cos2θ) / 60

[0018] Where, α m represents the geodetic latitude, δ represents the solar declination, Ω represents the solar hour angle, θ represents the day angle, S and F represent the hour value and minute value of the observation respectively, λ m represents the longitude of the observation point, λs Indicates the base longitude of the time zone, E q Indicates the difference between true solar time and mean solar time.

[0019] Furthermore, in step S2, the modified electron density model is expressed as:

[0020] N e (h)=a+b×(h-64),0≤h≤79km

[0021] N e (h)=y0+C×(coth(hx c )-1 / (hx c )),h>79km

[0022] Where N e (h) represents the function of electron density changing with time and space, a, b, y0, C and x c Both represent parameters that change with the solar zenith angle, and h represents the height above the ground.

[0023] Furthermore, in N e (h) = a + b × (h-64), when in the day-night transition zone, if N e (h)<0, then assign it a value of 0.

[0024] Furthermore, the modified electron density model further includes:

[0025] The parameters in the modified electron density model are calibrated by combining very low frequency electromagnetic wave simulation, actual testing and artificial intelligence prediction results.

[0026] Furthermore, in step S4, the training loss function of the artificial intelligence model is:

[0027]

[0028] Where, represents the amplitude or phase of the very low frequency electromagnetic wave simulated based on the FEM method, q i It represents the amplitude or phase predicted by the Elman neural network, and N represents the number of samples.

[0029] Furthermore, in step S4, the artificial intelligence model is an Elman neural network, and the number of neurons in its hidden layer is 32.

[0030] The beneficial effects of the present invention are:

[0031] (1) Compared with the relatively stable ionosphere during the day and night, the ionosphere in the transition zone changes relatively drastically. In this invention, by introducing the zenith angle and the modified electron density model, combined with the numerical simulation and experimental testing of VLF wave propagation, the constructed artificial intelligence model (Elman neural network) can quickly and accurately predict the electron density in the day-night transition zone of the ionosphere D region.

[0032] (2) The modified electron density model proposed in the present invention is a segmented straight line and Langevin function that varies with the zenith angle, which can analytically express and accurately reflect the spatiotemporal variation of the electron density in the lower ionosphere.

[0033] (3) The artificial intelligence model proposed in the present invention is based on the solar zenith angle and the modified electron density model combined with the FEM method to generate a training data set for numerical simulation. It is highly efficient and stable when used to predict the amplitude and phase propagation characteristics of electromagnetic waves and invert the electron density in the lower ionosphere.

[0034] (4) Compared with the results of traditional complex IRI models and EFM numerical simulations, the electromagnetic wave amplitude and phase propagation characteristics predicted by the inverted low ionospheric electron density obtained in the present invention are in good agreement with the measured results, which can provide strong technical support for the study of the propagation characteristics of very low frequency signals in the Earth-ionosphere waveguide structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Flowchart of the electron density inversion method for the day-night transition zone provided by the present invention.

[0036] Figure 2 The simulation results of the electric field r component amplitude and phase changing with the modified electron density model parameters provided by the present invention; where (a) UT=12, (b) UT=24.

[0037] Figure 3 The inverted electron density during the day-night transition period provided by the present invention changes with the solar zenith angle and altitude above the ground; wherein, (a) is the sunrise-corrected electron density model; (b) is the sunset-corrected electron density model.

[0038] Figure 4 The JXN platform provided by the present invention is Taiwan E r Numerical simulation and test results of component amplitude and phase. DETAILED DESCRIPTION

[0039] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0040] The embodiment of the present invention provides a method for inverting electron density in the day-night transition zone, such as Figure 1 As shown, the following steps are included:

[0041] S1, extracting the solar zenith angle of any transmission path of very low frequency electromagnetic waves;

[0042] S2. Based on the IRI model, the electron density is fitted with the variation of the solar zenith angle and the altitude above the ground, and a modified electron density model containing a straight line and a Langevin function is obtained, which is suitable for the lower ionosphere to characterize the variation of the electron density with time and space;

[0043] S3. Introducing Universal Time, the solar zenith angle, and the modified electron density model into the Earth-ionosphere waveguide model constructed based on the FEM method, numerical simulations were used to generate very low frequency electromagnetic wave propagation datasets under different spatiotemporal distributions of electron density.

[0044] S4. Using the very low frequency electromagnetic wave propagation dataset to train the artificial intelligence model, an electron density inversion model is obtained that reflects the mapping relationship between the parameters in the modified electron density model and the very low frequency electromagnetic wave propagation;

[0045] S5. Input the test amplitude and phase of the very low frequency electromagnetic waves in the day-night transition zone that change with the universal time into the electron density inversion model, and invert the spatiotemporal distribution of the electron density in the ionosphere D region along the very low frequency electromagnetic wave propagation path.

[0046] In step S1 of the embodiment of the present invention, the solar zenith angle χ at any position is:

[0047] χ=90°-H

[0048] Wherein, the solar altitude angle H is H=0° at sunrise and sunset on the horizon, H>0° during the day, and H<0° at night, which satisfies:

[0049] sinH=cosα m cosδcosΩ+sinα m sinδ

[0050] δ=0.3723+23.2567sinθ+0.1149sin2θ

[0051] -0.1712sin3θ-0.758cosθ+0.3656cos2θ+0.0201cos3θ

[0052] Ω=15[S+F / 60+(λ m -λ s ) / 15+E q -12]

[0053] E q =(0.0028-1.9857sinθ+9.9059sin2θ-7.0924cosθ-0.6882cos2θ) / 60

[0054] Where, α m represents the geodetic latitude, δ represents the solar declination, Ω represents the solar hour angle, which is defined as the angular difference between the local true solar time of the observation station and noon, θ represents the day angle, S and F represent the hour and minute values ​​of the observation respectively, and λ m represents the longitude of the observation point, λ s Indicates the base longitude of the time zone, E q Indicates the difference between true solar time and mean solar time.

[0055] Based on this, in this embodiment, the time difference between mean solar time and true solar time can be solved based on the relationship between the solar altitude angle, geodetic latitude, solar declination, solar hour angle and zenith angle at any position, and the observation point accuracy in degrees is converted into the time difference with Greenwich. After a series of solutions, the time-varying and space-varying solar zenith angle on the great circle path of VLF wave propagation determined by the transmitting station and the receiving station is obtained.

[0056] In step S2 of this embodiment of the present invention, the distribution of electron density as a function of altitude and solar zenith angle in the IRI model along the VLF propagation path at a specific moment (different locations correspond to different solar zenith angles) is extracted using offline Fortran software. The variation of electron density as a function of altitude in multiple zenith angle IRI models is fitted using Origin software. A modified electron density model is derived and proposed that reflects the variation of electron density over time and space, i.e., the variation with solar zenith angle and altitude. This model is expressed as:

[0057] N e (h)=a+b×(h-64),0≤h≤79km

[0058] N e (h)=y0+C×(coth(hx c )-1 / (hx c )),h>79km

[0059] Where N e(h) represents the function of electron density changing with time and space, a, b, y0, C and x c Both represent parameters that change with the solar zenith angle, and h represents the height above the ground.

[0060] In this embodiment, N e (h) = a + b × (h-64), when in the day-night transition zone, if N e (h)<0, then assign it a value of 0.

[0061] In this embodiment, the modified electron density model further includes:

[0062] The parameters in the modified electron density model are calibrated by combining very low frequency electromagnetic wave simulation, actual testing and artificial intelligence prediction results.

[0063] In a specific example of this embodiment, Figure 2 As shown in the figure, the simulation results of the electric field r component amplitude and phase changing with the modified electron density model parameters are given. Figure 2 (a) and Figure 2 (b) The time is given as UT = 12 o'clock and UT = 24 o'clock respectively. Frequency domain finite element method simulation results of the Er component amplitude and phase of the very low frequency 16.4kHz signal received by the station (78.9167°N, 11.9333°E) from the JXN station (66.9744°N, 13.8736°E) as the various parameters of the corrected electron density model change. Figure 2 The phase shown in the figure is improved by 203.8° based on the simulation results. Figure 2 (a) y0 = 14059.8, C = 14958.5, x c =90.739km, Figure 2 (b) where b = 22, C = 7816.1, x c = 98.4 km. As can be seen from the figure, generally speaking, as the ionospheric electron density decreases (a, b, or y0 decreases), the amplitude of the VLF wave increases and the phase decreases. In the day-night transition zone, the changes in amplitude and phase are more obvious, and the changes between day and night are relatively small.

[0064] The numerical simulation results based on the IRI model show that JXN to The 16.4kHz signal penetrates the ionosphere to depths of approximately 75km and 93km during the day and night, respectively. Therefore, parameter changes in the Langevin function in the daytime electron density correction model have almost no effect on VLF signal propagation, while parameter changes in the nighttime linear function have no effect on VLF wave propagation. Therefore, a = 30 and b = 21.4 are selected as the parameters of the daytime electron density correction model, corresponding to the simulated VLF amplitude and phase of -41.6dB and -68.9°, respectively. Figure 2 (a) corresponds to the data +203.8°); a=b=0, y0=7265.3, C=7816.1 and x c =98.4km is the parameter of the night-time corrected electron density model, and the corresponding VLF amplitude and phase are -35.7dB and -133.3° respectively. Figure 2 The corresponding data in (b) is +203.8°).

[0065] In step S4 of the embodiment of the present invention, the training loss function of the artificial intelligence model is:

[0066]

[0067] Where, represents the amplitude or phase of the very low frequency electromagnetic wave simulated based on the FEM method, q i It represents the amplitude or phase predicted by the Elman neural network, and N represents the number of samples.

[0068] In step S4 of the embodiment of the present invention, the artificial intelligence model may be an Elman neural network, and the number of neurons in its hidden layer is 32.

[0069] Specifically, in a specific example of an embodiment of the present invention, taking the Elman neural network as an artificial intelligence model for inverting electron density as an example, the effect of the number of hidden layer neurons in the Elman neural network on the amplitude and phase mean square error at different times is shown in Table 1;

[0070] Table 1:

[0071]

[0072] Table 1 compares the impact of the number of hidden layer neurons on the AI's performance in predicting VLF wave amplitude and phase at 18, 19, and 20 UT. A data set of 729 samples (679 training samples and 50 test samples) with different parameters for the modified electron density model was generated based on frequency-domain FEM simulations. The maximum number of iterations in the Elman neural network parameters was 1000, and the learning rate was 0.001. When generating the data set based on frequency-domain FEM, the parameters of the piecewise straight line and Langevin function for the modified electron density model of the Earth-ionosphere waveguide generally adhere to the principle that the higher the altitude, the smaller the zenith angle, and the greater the electron density. As shown in Table 1, considering both the AI's prediction accuracy and time cost, the number of hidden layer neurons can be set to 32.

[0073] In an embodiment of the present invention, based on the above electron density inversion method, such as Figure 3 As shown in FIG, the variation of electron density during sunrise and sunset with the solar zenith angle and altitude from the ground obtained based on the method of the present invention is given, wherein 3(a) is the inverted sunrise corrected electron density model, and 3(b) is the inverted sunset corrected electron density model. Compared with the traditional IRI model, the VLF amplitude and phase prediction results obtained by the present invention based on the corrected electron density model represented by straight lines and Langevin segments combined with artificial intelligence are more consistent with the measured results in the day-night transition zone, which to a certain extent reflects that the electron density distribution of the corrected electron density model at an altitude of 65-93 km during the day-night transition period is more reasonable.

[0074] Figure 4 March 18, 2020 Daily variations of the amplitude and phase of the 16.4kHz signal received by the station from the JXN station. The stratum of the waveguide structure in the numerical simulation is seawater, and the relative dielectric constant ε r =70Conductivityσ=5S / m. Figure 4 The experimental data from the literature (Thomson et al., 2021), the frequency domain FEM combined with the IRI model simulation and the artificial intelligence prediction results based on the modified electron density model were compared. Compared with the simulation results of the frequency domain FEM combined with the modified electron density model, the change trend of the artificial intelligence prediction results and the experimental results is more consistent. Figure 4It can be seen that although the amplitude and phase simulated by the frequency domain FEM combined with the IRI model can reflect the changes in the day-night transition zone to a certain extent, the sunrise effect is too early, the sunset effect is too late, and the transition period appears to be too long. The VLF amplitude and phase errors predicted based on the corrected electron density model combined with the artificial intelligence model in the present invention are less than 0.2 dB and 2.4 degrees respectively during the day-night transition period. It can more accurately capture the changing trends of the VLF amplitude and phase during the day-night transition period, and more accurately predict the propagation characteristics of the VLF electromagnetic waves. In addition, artificial intelligence prediction has the advantage of fast speed.

[0075] Specific embodiments are used in the present invention to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

[0076] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A method for inverting electron density in the day-night transition zone, characterized in that: The following steps are involved: S1, extracting the solar zenith angle of any transmission path of very low frequency electromagnetic waves; S2. Based on the IRI model, the electron density is fitted with the variation of the solar zenith angle and the altitude above the ground, and a modified electron density model containing a straight line and a Langevin function is obtained, which is suitable for the lower ionosphere to characterize the variation of the electron density with time and space; S3. Introducing Universal Time, the solar zenith angle, and the modified electron density model into the Earth-ionosphere waveguide model constructed based on the FEM method, numerical simulations were used to generate very low frequency electromagnetic wave propagation datasets under different spatiotemporal distributions of electron density. S4. Using the very low frequency electromagnetic wave propagation dataset to train the artificial intelligence model, an electron density inversion model is obtained that reflects the mapping relationship between the parameters in the modified electron density model and the very low frequency electromagnetic wave propagation; S5. Input the test amplitude and phase of the very low frequency electromagnetic waves in the day-night transition zone that change with the universal time into the electron density inversion model, and invert the spatiotemporal distribution of the electron density in the ionosphere D region along the very low frequency electromagnetic wave propagation path.

2. The electron density inversion method for the day-night transition zone according to claim 1, characterized in that: In step S1, the solar zenith angle χ at any position is: χ=90°-H Where H represents the solar altitude angle, which satisfies: sinH=cosα m cosδcosΩ+sinα m sinδ δ=0.3723+23.2567sinθ+0.1149sin2θ -0.1712sin3θ-0.758cosθ+0.3656cos2θ+0.0201cos3θ Ω=15[S+F / 60+(λ m -l s ) / 15+E q -12] E q =(0.0028-1.9857sinθ+9.9059sin2θ-7.0924cosθ-0.6882cos2θ) / 60 Where, α m represents the geodetic latitude, δ represents the solar declination, Ω represents the solar hour angle, θ represents the day angle, S and F represent the hour value and minute value of the observation respectively, λ m represents the longitude of the observation point, λ s Indicates the base longitude of the time zone, E q Indicates the difference between true solar time and mean solar time.

3. The electron density inversion method for the day-night transition zone according to claim 1, characterized in that: In step S2, the modified electron density model is expressed as: N e (h)=a+b×(h-64),0≤h≤79km N e (h)=y0+C×(coth(hx c )-1 / (hx c )),h>79km Where N e (h) represents the function of electron density changing with time and space, a, b, y0, C and x c Both represent parameters that change with the solar zenith angle, and h represents the height above the ground.

4. The method for inverting electron density in the day-night transition zone according to claim 3, characterized in that: In N e (h) = a + b × (h-64), when in the day-night transition zone, if N e (h)<0, then assign it a value of 0.

5. The method for inverting electron density in the day-night transition zone according to claim 3, characterized in that: The modified electron density model also includes: The parameters in the modified electron density model are calibrated by combining very low frequency electromagnetic wave simulation, actual testing and artificial intelligence prediction results.

6. The method for inverting electron density in the day-night transition zone according to claim 1, characterized in that: In step S4, the training loss function of the artificial intelligence model is: Where, represents the amplitude or phase of the very low frequency electromagnetic wave simulated based on the FEM method, q i It represents the amplitude or phase predicted by the Elman neural network, and N represents the number of samples.

7. The method for inverting electron density in the day-night transition zone according to claim 1, characterized in that: In step S4, the artificial intelligence model is an Elman neural network, and the number of neurons in its hidden layer is 32.

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