A low-ionosphere ws parameter very low frequency inversion method and system based on GRU-HSWOA time series modeling

Abstract

This invention discloses a method and system for very low frequency (VLS) inversion of low ionospheric WS parameters based on GRU-HSWOA time-series modeling. The method includes: acquiring VLS observation data, demodulating and preprocessing it, and extracting amplitude time series; calculating initial values ​​of WS parameters based on an empirical solar zenith angle model, and introducing perturbations to generate enhanced parameter samples; inputting an electron density model to construct an electron density profile, obtaining the corresponding amplitude values ​​through numerical forward modeling, establishing a forward mapping from WS parameters to amplitude values, and forming sample pairs for inversion training; performing Z-score standardization and constructing time-series training samples using a sliding time window; constructing a time-series inversion network based on a gated recurrent unit (GRU), and adaptively optimizing the learning rate of the network using a hybrid strategy whale optimization algorithm (HSWOA) to obtain a trained inversion model; extracting amplitude time series from actual observation data, inputting it into the inversion model, and outputting low ionospheric WS parameters to achieve inversion.

Description

Technical Field

[0001] This invention belongs to the field of space electromagnetic detection and ionospheric remote sensing technology, specifically relating to a method and system for very low frequency inversion of low ionospheric WS parameters based on GRU-HSWOA time series modeling. Background Technology

[0002] The ionosphere is typically divided into regions D (60–90 km), E (90–130 km), and F (above 130 km). The lower part of regions D and E (approximately 60–120 km) is often referred to as the low ionosphere. Variations in its electron density significantly affect the propagation of low-frequency / very low-frequency radio waves in the Earth-ionospheric waveguide, thus impacting communications, navigation, and space weather forecasting. Because the low ionosphere lies between aircraft flight altitudes and satellite orbits, conventional in-situ detection is difficult; altimeters and incoherent scattering radars have insufficient coverage below 90 km, making continuous monitoring data of the low ionosphere challenging.

[0003] During propagation, the amplitude and phase of very low frequency (VLF) electromagnetic waves are modulated by the ionosphere. The observed amplitude / phase perturbations carry low ionospheric information. Therefore, retrieving ionospheric parameters from VLF observations is a nonlinear inverse problem. Traditional lookup table or least squares fitting methods require manually setting rules, have low computational efficiency, and are sensitive to noise, making them unsuitable for large-scale or long-term monitoring.

[0004] Existing studies have introduced deep learning to improve inversion efficiency, but many methods focus on reconstructing the spatial distribution of the ionosphere using spatially gridded multi-source observations; these methods mainly solve the problem of spatial correlation modeling and are dependent on the spatial coverage of observation points. Summary of the Invention

[0005] To address the problems of insufficient utilization of amplitude time series information, inadequate noise resistance and stability in existing technologies, the present invention aims to overcome the above-mentioned defects of existing technologies and proposes a very low frequency inversion method and system for low ionospheric WS parameters based on GRU-HSWOA time series modeling, and realizes continuous monitoring of low ionospheric WS parameters.

[0006] In view of this, the present invention proposes a very low frequency inversion method for low ionospheric WS parameters based on GRU-HSWOA time series modeling, comprising: Step 1: Acquire very low frequency observation data, demodulate and preprocess it, and extract the amplitude time series; Step 2: Calculate the initial values ​​of the WS parameters based on the empirical model of solar zenith angle, and introduce perturbations to generate enhanced parameter samples based on the initial values; the WS parameters include equivalent reflection height and sharpness; Step 3: Input the enhanced parameter samples into the electron density model, construct the electron density profile, and obtain the corresponding amplitude values ​​through numerical forward modeling, thereby establishing a forward mapping from WS parameters to amplitude values ​​and forming sample pairs for inversion training; Step 4: Standardize the amplitude values ​​in the sample pairs using Z-score and construct time-series training samples using a sliding time window; Step 5: Construct a time-series inversion network based on gated recurrent units (GRUs), and train it using time-series training samples. During the training process, the learning rate of the time-series inversion network is adaptively optimized using the hybrid strategy whale optimization algorithm (HSWOA) to obtain the trained inversion model. Step 6: After demodulating and preprocessing the actual observation data, extract the amplitude time series, input it into the trained inversion model, and output the low ionosphere WS parameters to achieve inversion.

[0007] As an improvement to the above method, the demodulation in steps 1 and 6 both adopt the minimum frequency shift keying (MSK) demodulation method; the preprocessing includes: quality screening and extraction of amplitude time series with equal time intervals.

[0008] As an improvement to the above method, step 2 introduces a perturbation to generate enhanced parameter samples based on the initial values, including: For equivalent reflection height Introducing the first disturbance , Regarding sharpness Introducing a second disturbance The enhanced equivalent reflection height is obtained. and sharpness : , .

[0009] As an improvement to the above method, before introducing perturbations to generate enhanced parameter samples based on the initial values ​​in step 2, the method further includes: applying physical interval soft constraints to the WS parameters. The soft constraint adopts a smoothing constraint mechanism based on the hyperbolic tangent function, satisfying the following equation:

[0010] in, This represents the ionospheric WS parameter values ​​calculated based on an empirical model and before physical constraint treatment. This indicates the values ​​of the WS parameters after soft constraint processing; This represents the center value of the physically reasonable range of the WS parameter. This represents half the range of the physical interval, parameter Used to adjust the strength of soft constraint.

[0011] As an improvement to the above method, the electron density profile constructed in step 3 for:

[0012] in, Indicates altitude, express At a high altitude Electron density profile at , in units of ; Numerical forward modeling uses the long-wavelength propagation model LWPC; The sample pairs for inversion training are: ,in This represents the amplitude value; the number of sample pairs shall not be less than 10,000.

[0013] As an improvement to the above method, the sliding time window in step 4 has a window length of 10 time points and a step size of 1 time point.

[0014] As an improvement to the above method, the time-series inversion network constructed in step 5 includes: The first layer contains 64 hidden units, which are used to process multi-dimensional time series inputs composed of very low frequency amplitude features and extract temporal evolution features within a sliding time window. The second layer contains 32 hidden units, which are used to compress and refine the temporal features output from the previous layer. Fully connected layer: contains 32 neurons and uses the ReLU activation function; Output layer: Output equivalent reflection height With sharpness .

[0015] As an improvement to the above method, the training in step 5 uses a training set, which is divided into a training set and a test set, with 80% of the time-series training samples divided into 20% in chronological order. The 20% in the training set is then divided into a validation set. The mean squared error (MSE) is used as the loss function, and the Adam optimizer is used for training. The batch size is 32, the maximum number of training epochs is 100, and an early stopping mechanism is set: if the validation set loss does not decrease for 15 consecutive training epochs, training is stopped and rolled back to the optimal weights.

[0016] As an improvement to the above method, in step 5, the learning rate of the time-series inversion network is adaptively optimized using the Hybrid Strategy Whale Optimization Algorithm (HSWOA), and its search interval is set to... Based on the standard whale optimization algorithm, the following improvement strategies were introduced: The initial search entity is generated using a Logistic chaotic mapping. During the search process, the Lévy flight strategy was introduced; When the search stalls, a mutation operator based on the Cauchy distribution is introduced to perturb the individuals in the population.

[0017] On the other hand, the present invention provides a very low frequency inversion system for low ionospheric WS parameters based on GRU-HSWOA time series modeling, comprising: The data acquisition and preprocessing module is used to acquire very low frequency observation data, demodulate and preprocess it, and extract the amplitude time series. An enhanced parameter sample generation module is used to generate enhanced parameter samples based on the initial values ​​of the solar zenith angle empirical model WS parameters and by introducing perturbations on the basis of the initial values; the WS parameters include equivalent reflection height and sharpness; The inversion sample pair generation module is used to input the enhanced parameter samples into the electron density model, construct the electron density profile, and obtain the corresponding amplitude values ​​through numerical forward modeling, thereby establishing a forward mapping from WS parameters to amplitude values ​​and forming sample pairs for inversion training. The time-series sample construction module is used to standardize the amplitude values ​​in the sample pairs using Z-score and construct time-series training samples using a sliding time window. The model building and training module is used to construct a time-series inversion network based on a gated recurrent unit (GRU). It employs time-series training samples for training. During training, the learning rate of the time-series inversion network is adaptively optimized using a hybrid strategy whale optimization algorithm (HSWOA) to obtain the trained inversion model. The inversion output module is used to input the amplitude time series of the actual observation data processed by the data acquisition and preprocessing module into the trained inversion model, and output the low ionosphere WS parameters to achieve inversion.

[0018] Compared with the prior art, the advantages of the present invention are: 1. Modeling VLF inversion as a time series problem can improve the stability of the inversion results by utilizing the correlation characteristics between adjacent moments in the amplitude time series.

[0019] 2. The GRU structure is adopted to enhance the expression of time-dependent features while ensuring computational efficiency; 3. By automatically optimizing the learning rate through HSWOA, the dependence on manual parameter tuning is reduced and the convergence stability is improved; 4. Combine physical forward modeling to generate samples to improve the applicability of the model under different solar zenith angle conditions.

[0020] 5. Introducing a physical interval soft constraint mechanism can further improve the physical consistency of training samples. Attached Figure Description

[0021] Figure 1 This is a flowchart of the GRU inversion model and HSWOA optimization. Figure 2 These are the training and validation loss curves of the GRU-HSWOA time-series inversion model in this embodiment of the invention; Figure 3 shows the diurnal variation characteristics of the low-ionospheric WS parameters and electron density obtained from the very low frequency amplitude time series inversion. Among them, Figure 3(a) shows the equivalent reflection height. The change over time; Figure 3(b) shows the sharpness. The time variation; Figure 3(c) shows the electron density height-time distribution calculated based on the inversion parameters. Detailed Implementation

[0022] This invention provides a method for very low frequency (VLF) inversion of low ionospheric WS parameters based on GRU-HSWOA time-series modeling. This method uses the signal amplitude acquired by a ground-based VLF receiving system as the observation, and treats ionospheric parameter inversion modeling as a time-series inversion problem. It constructs amplitude time-series samples through a sliding time window and employs a gated recurrent neural network to extract time-related features in amplitude changes, thereby realizing the equivalent reflection height of the ionospheric WS parameters. With sharpness The inversion.

[0023] During the construction of training samples, the equivalent reflection height of the low ionospheric WS parameters is calculated based on the empirical model of solar zenith angle. and sharpness In one embodiment, the initial values ​​of the parameters can be optionally smoothed by a soft constraint mechanism based on the hyperbolic tangent function. Based on this, parameter perturbations are introduced, and training samples are generated by combining the ionospheric electron density model and the very low frequency (VLF) wave propagation forward model. The inversion model uses a gated recurrent unit (GRU) to construct a temporal neural network, and employs the Hybrid Strategy Whale Optimization Algorithm (HSWOA) to adaptively optimize the model learning rate, thereby achieving stable inversion of the low ionospheric WS parameters, suitable for continuous monitoring of the low ionospheric region.

[0024] Specifically, it includes: Step 1: Acquire very low frequency observation data, demodulate and preprocess it, and extract the amplitude time series; Step 2: Calculate the initial values ​​of the WS parameters based on the empirical model of solar zenith angle, and introduce perturbations to generate enhanced parameter samples based on the initial values; the WS parameters include equivalent reflection height and sharpness; The empirical model for the solar zenith angle is as follows:

[0025]

[0026] Where X is the solar zenith angle. For the equivalent reflection height, For sharpness.

[0027] Step 3: Input the enhanced parameter samples into the electron density model, construct the electron density profile, and obtain the corresponding amplitude values ​​through numerical forward modeling, thereby establishing a forward mapping from WS parameters to amplitude values ​​and forming sample pairs for inversion training; Step 4: Standardize the amplitude values ​​in the sample pairs using Z-score and construct time-series training samples using a sliding time window; Step 5: Construct a time-series inversion network based on gated recurrent units (GRUs), and train it using time-series training samples. During the training process, the learning rate of the time-series inversion network is adaptively optimized using the hybrid strategy whale optimization algorithm (HSWOA) to obtain the trained inversion model. Step 6: After demodulating and preprocessing the actual observation data, extract the amplitude time series, input it into the trained inversion model, and output the low ionosphere WS parameters to achieve inversion.

[0028] Invention point: (1) Based on MSK demodulation, the amplitude time series is obtained and high-quality samples are selected. Only the amplitude is used as the observation. (2) Training sample pairs are generated by combining the SZA empirical model, parameter perturbation, Wait-Spies electron density model and LWPC forward modeling; (3) Using GRU time-series neural network to realize amplitude sequence to The inversion; (4) Use HSWOA to adaptively optimize the learning rate and improve convergence stability.

[0029] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0030] Example 1 Embodiment 1 of the present invention provides a very low frequency inversion method for low ionospheric WS parameters based on GRU-HSWOA time series modeling, the specific steps of which are as follows: Observational data acquisition and processing: This embodiment uses a Japanese JJI transmitter as the VLF signal source, located at (131°04′E, 32°01′N), operating at a frequency of 22.2 kHz, with a transmit power of approximately 200 kW. The receiver is a ground-based VLF receiving system at the Suizhou station in Hubei, China (113°32′E, 31°57′N). The propagation path length between the transmitter and receiver is approximately 1568.3 km, which is considered short-path propagation. The observation data covers the daytime period (09:00–16:00 LT) from 2018 to 2022. The received signal was demodulated using MSK to obtain amplitude and phase. Since the phase information is unstable, only the amplitude was used as the inversion observation.

[0031] Training data generation: To train the machine learning inversion model, synthetic training samples are generated. First, based on the SZA empirical model proposed by McRae and Thomson, the SZA at different time points is calculated. and Initial value.

[0032] In an optional implementation, to ensure the physical validity of the training samples, a soft constraint on the parameters can be applied to a physical interval before introducing perturbations. The soft constraint employs a smoothing constraint mechanism based on the hyperbolic tangent function, and its expression is:

[0033] in, This represents the ionospheric WS parameter values ​​calculated based on an empirical model and before physical constraint treatment. This indicates the values ​​of the WS parameters after soft constraint processing; This represents the center value of the physically reasonable range of the WS parameter. This represents half the range of the physical interval, parameter Used to adjust the strength of soft constraints. When the parameter value is within the physical range, the soft constraint has little effect on the parameter; when the parameter value is close to or exceeds the boundary of the physical range, the constraint function gradually tends to saturate, thereby limiting the range of parameter change and preventing abnormal parameters from entering the non-physical value range.

[0034] To improve sample diversity, a perturbation is introduced:

[0035] Substitute the perturbation parameters into the Wait–Spies model to construct the electron density profile:

[0036] Then, using different parameter combinations as input, LWPC is called to calculate the VLF amplitude (Amp) under a specific propagation path, establishing a forward mapping. Thus constructing inversion sample pairs By traversing different SZA conditions and applying perturbations, 10,000 sets of mapping samples were generated for training and validating the inversion model.

[0037] GRU time-series inversion network structure: The inversion network employs a two-layer stacked gated recurrent unit structure: the first layer contains 64 hidden units, used to process the multidimensional time-series input composed of very low frequency amplitude features and extract the temporal evolution features within a sliding time window; the second layer contains 32 hidden units, used to compress and refine the temporal features output from the previous layer; subsequently, a fully connected layer containing 32 neurons is connected and a ReLU activation function is used; the output layer has two output nodes, corresponding to the equivalent reflection height. With sharpness .

[0038] Time-series sample construction and training strategy: Input features are standardized using Z-scores; samples are constructed using a sliding time window with a window length of 10 and a step size of 1; data is divided into a training set (80%) and a test set (20%) in chronological order. The 20% of the training set is then used as a validation set. Model training employs the MSE loss function and the Adam optimizer, with a batch size of 32 and a maximum training epoch of 100; an early stopping mechanism is implemented: if the validation set loss does not decrease for 15 consecutive epochs, training is stopped and the model reverts to the optimal weights.

[0039] HSWOA learning rate adaptive optimization: To further improve the convergence accuracy and training stability of the GRU time-series inversion model, in one embodiment, a hybrid strategy whale optimization algorithm (HSWOA) is introduced to adaptively optimize the learning rate parameter during the model training process.

[0040] In the learning rate optimization process, the learning rate is the only hyperparameter to be optimized, and its search range is set to... The population size of HSWOA is set to 30, and the maximum number of iterations is 100, in order to complete the search of the learning rate parameter space with reasonable computational overhead.

[0041] In the algorithm initialization phase, Logistic chaotic mapping is used to generate initial search individuals, and the chaotic control parameters are set to... To enhance the traversal of individuals within the search space at the initial learning rate, a Lévy flight strategy is introduced to improve the spiral search phase of the whale algorithm during the search process. The Lévy parameter is set to 1.5, and the search range of the learning rate parameter is expanded by combining long and short step sizes. When the search process stalls, a mutation operator based on Cauchy distribution is introduced to perturb the search individuals, with the mutation strength parameter set to 0.0001 to reduce the probability of the search process getting trapped in local optima.

[0042] During the optimization process, each search individual corresponds to a candidate learning rate parameter, and a corresponding GRU inversion model is built and trained based on this learning rate. The mean squared error on the validation set is used as the fitness function to evaluate the training effect of the model corresponding to different learning rates. When the optimization process meets the convergence condition, the learning rate parameter with the best fitness is selected and used to train the final GRU time-series inversion model, thereby achieving adaptive configuration of the learning rate parameter.

[0043] The flowchart of GRU inversion model and HSWOA optimization is as follows: Figure 1 As shown.

[0044] Example 2 Embodiment 2 of the present invention provides a very low frequency inversion system for low ionospheric WS parameters based on GRU-HSWOA time series modeling, implemented based on the method of Embodiment 1. The system includes: The data acquisition and preprocessing module is used to acquire very low frequency observation data, demodulate and preprocess it, and extract the amplitude time series. An enhanced parameter sample generation module is used to generate enhanced parameter samples based on the initial values ​​of the solar zenith angle empirical model WS parameters and by introducing perturbations on the basis of the initial values; the WS parameters include equivalent reflection height and sharpness; The inversion sample pair generation module is used to input the enhanced parameter samples into the electron density model, construct the electron density profile, and obtain the corresponding amplitude values ​​through numerical forward modeling, thereby establishing a forward mapping from WS parameters to amplitude values ​​and forming sample pairs for inversion training. The time-series sample construction module is used to standardize the amplitude values ​​in the sample pairs using Z-score and construct time-series training samples using a sliding time window. The model building and training module is used to construct a time-series inversion network based on the gated recurrent unit (GRU). It is trained using time-series training samples. During the training process, the learning rate of the time-series inversion network is adaptively optimized using the hybrid strategy whale optimization algorithm (HSWOA) to obtain the trained inversion model. The inversion output module is used to input the amplitude time series of the actual observation data processed by the data acquisition and preprocessing module into the trained inversion model, and output the low ionosphere WS parameters to achieve inversion.

[0045] It is worth noting that in the embodiments of the above system, the modules included are divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of each functional module are only for easy differentiation and are not used to limit the scope of protection of the present invention.

[0046] Experimental data 1: like Figure 2 The paper presents curves showing the changes in training set loss and validation set loss with training epochs during the training process of the GRU-HSWOA time-series inversion model based on the present invention, where the vertical axis represents the loss value (mean squared error) and the horizontal axis represents the training epoch.

[0047] As can be seen from the figure, in the early stage of training, both the training set loss and the validation set loss decrease rapidly with the increase of training rounds, indicating that the model parameters can converge effectively in the initial stage. As the number of training rounds increases further, the rate of decrease of both gradually slows down and tends to stabilize after about the 6th to 8th training rounds, with the loss value remaining at a low level.

[0048] Meanwhile, it can be observed that the trend of the validation set loss is basically consistent with that of the training set loss throughout the training process, without any obvious divergence or reverse increase, indicating that the model did not experience significant overfitting during training and that the training process has good stability.

[0049] The above training process shows that, with the adaptive optimization of the learning rate by the hybrid strategy whale optimization algorithm, the GRU time series inversion model can achieve stable convergence within a limited number of training rounds, and is suitable for subsequent inversion applications of very low frequency amplitude time series.

[0050] Experimental data 2: Figures 3(a)–3(c) show the WS parameters of the low ionosphere obtained by inversion based on the method of the present invention and their corresponding electron density height-time distribution results, which are used to illustrate the characterization of the evolution of the low ionosphere under continuous daytime observation conditions.

[0051] As shown in Figure 3(a), the equivalent reflection height of the lower ionosphere The data exhibits a clear temporal variation during the daytime period (09:00–16:00). The solid line represents the median curve of the inversion results, and the dashed line represents the interquartile range (Q1–Q3) of the inversion results. It can be seen that... It gradually decreases during the morning, reaching a relatively low height near noon; then it gradually increases during the afternoon.

[0052] As shown in Figure 3(b), the low-ionospheric sharpness obtained by inversion within the same time period The variation over time shows a pattern of gradually increasing in the morning, reaching a high level near noon, and gradually decreasing in the afternoon. Throughout the entire time period, The changes were continuous, with no abrupt changes.

[0053] Based on the above inversion... and The parameters were further used to calculate the electron density distribution at different altitudes in the lower ionosphere using the ionospheric electron density model, as shown in Figure 3(c). It can be seen that in the altitude range of 60–90 km, the electron density is generally higher near noon, with the most significant change occurring in the altitude range of 70–85 km; as time transitions from noon to afternoon, the electron density generally shows a gradually decreasing trend.

[0054] As can be seen from the results in Figures 3(a)–(c), the method of the present invention can stably retrieve the WS parameters of the low ionosphere under continuous observation conditions, and further realize the reconstruction of the electron density height structure of the low ionosphere, which is suitable for continuous monitoring of the diurnal variation process of the low ionosphere during the daytime.

[0055] Description of method stability and continuous monitoring capability: The experimental data above demonstrate that the method of this invention exhibits good temporal consistency and continuity in the inversion results of the WS parameters of the D layer of the ionosphere over a continuous time period. By constructing very low frequency amplitude observation data into time series samples and using a gated recurrent neural network for time series modeling, the characteristics of amplitude evolution over time can be fully characterized, ensuring that the inversion results remain stable under continuous observation conditions and avoiding parameter fluctuations that may occur in single-time-point inversions.

[0056] In summary, the present invention proposes a very low frequency inversion method and system for low ionospheric WS parameters based on GRU-HSWOA time-series modeling, which can stably invert the equivalent reflectance height under continuous daytime observation conditions. and sharpness Furthermore, the method reconstructs the height-time distribution of electron density. The inversion results show smooth changes over time, consistent with the physical characteristics of diurnal variations in the low ionosphere, indicating that this method is suitable for quantitative analysis and continuous monitoring of diurnal variations in the low ionosphere.

[0057] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A very low frequency inversion method for low ionospheric WS parameters based on GRU-HSWOA time series modeling, comprising: Step 1: Acquire very low frequency observation data, demodulate and preprocess it, and extract the amplitude time series; Step 2: Calculate the initial values ​​of the WS parameters based on the empirical model of solar zenith angle, and introduce perturbations to generate enhanced parameter samples based on the initial values; the WS parameters include equivalent reflection height and sharpness; Step 3: Input the enhanced parameter samples into the electron density model, construct the electron density profile, and obtain the corresponding amplitude values ​​through numerical forward modeling, thereby establishing a forward mapping from WS parameters to amplitude values ​​and forming sample pairs for inversion training; Step 4: Standardize the amplitude values ​​in the sample pairs using Z-score and construct time-series training samples using a sliding time window; Step 5: Construct a time-series inversion network based on gated recurrent units (GRUs), and train it using time-series training samples. During the training process, the learning rate of the time-series inversion network is adaptively optimized using the hybrid strategy whale optimization algorithm (HSWOA) to obtain the trained inversion model. Step 6: After demodulating and preprocessing the actual observation data, extract the amplitude time series, input it into the trained inversion model, and output the low ionosphere WS parameters to achieve inversion.

2. The method for very low frequency inversion of low ionospheric WS parameters based on GRU-HSWOA time series modeling according to claim 1, characterized in that, The demodulation in steps 1 and 6 both adopt the minimum frequency shift keying (MSK) demodulation method; the preprocessing includes: quality screening and extraction of amplitude time series with equal time intervals.

3. The method for very low frequency inversion of low ionospheric WS parameters based on GRU-HSWOA time series modeling according to claim 1, characterized in that, Step 2 introduces a perturbation based on the initial values ​​to generate enhanced parameter samples, including: For equivalent reflection height Introducing the first disturbance , Regarding sharpness Introducing a second disturbance The enhanced equivalent reflection height is obtained. and sharpness : ， 。 4. The method for very low frequency inversion of low ionospheric WS parameters based on GRU-HSWOA time series modeling according to claim 1, characterized in that, Before step 2 introduces perturbations to generate enhanced parameter samples based on the initial values, the method further includes: applying physical interval soft constraints to the WS parameters; The soft constraint adopts a smoothing constraint mechanism based on the hyperbolic tangent function, satisfying the following equation: in, This represents the ionospheric WS parameter values ​​calculated based on an empirical model and before physical constraint treatment. This indicates the values ​​of the WS parameters after soft constraint processing; This represents the center value of the physically reasonable range of the WS parameter. This represents half the range of the physical interval, parameter Used to adjust the strength of soft constraint.

5. The method for very low frequency inversion of low ionospheric WS parameters based on GRU-HSWOA time series modeling according to claim 3, characterized in that, The electron density profile constructed in step 3 for: ， in, Indicates altitude, express At a high altitude Electron density profile at , in units of ; Numerical forward modeling uses the long-wavelength propagation model LWPC; The sample pairs for inversion training are: ,in This represents the amplitude value; the number of sample pairs shall not be less than 10,000.

6. The method for very low frequency inversion of low ionospheric WS parameters based on GRU-HSWOA time series modeling according to claim 1, characterized in that, The sliding time window in step 4 has a length of 10 time points and a step size of 1 time point.

7. The method for very low frequency inversion of low ionospheric WS parameters based on GRU-HSWOA time series modeling according to claim 1, characterized in that, The time-series inversion network constructed in step 5 includes: The first layer contains 64 hidden units, which are used to process multi-dimensional time series inputs composed of very low frequency amplitude features and extract temporal evolution features within a sliding time window. The second layer contains 32 hidden units, which are used to compress and refine the temporal features output from the previous layer. Fully connected layer: contains 32 neurons and uses the ReLU activation function; Output layer: Output equivalent reflection height With sharpness .

8. The method for very low frequency inversion of low ionospheric WS parameters based on GRU-HSWOA time series modeling according to claim 1, characterized in that, The training in step 5 uses a training set, which is divided into a training set and a test set. Then, the 20% of the time-series training samples are divided into a validation set. The mean squared error (MSE) is used as the loss function, and the Adam optimizer is used for training. The batch size is 32, the maximum number of training epochs is 100, and an early stopping mechanism is set: if the validation set loss does not decrease for 15 consecutive training epochs, training is stopped and rolled back to the optimal weights.

9. The method for very low frequency inversion of low ionospheric WS parameters based on GRU-HSWOA time series modeling according to claim 1, characterized in that, In step 5, the learning rate of the time-series inversion network is adaptively optimized using the Hybrid Strategy Whale Optimization Algorithm (HSWOA), with its search interval set as follows: Based on the standard whale optimization algorithm, the following improvement strategies were introduced: The initial search entity is generated using a Logistic chaotic mapping. During the search process, the Lévy flight strategy was introduced; When the search stalls, a mutation operator based on the Cauchy distribution is introduced to perturb the individuals in the population.

10. A very low frequency inversion system for low ionospheric WS parameters based on GRU-HSWOA time series modeling, characterized in that, include: The data acquisition and preprocessing module is used to acquire very low frequency observation data, demodulate and preprocess it, and extract the amplitude time series. An enhanced parameter sample generation module is used to generate enhanced parameter samples based on the initial values ​​of the solar zenith angle empirical model WS parameters and by introducing perturbations on the basis of the initial values; the WS parameters include equivalent reflection height and sharpness; The inversion sample pair generation module is used to input the enhanced parameter samples into the electron density model, construct the electron density profile, and obtain the corresponding amplitude values ​​through numerical forward modeling, thereby establishing a forward mapping from WS parameters to amplitude values ​​and forming sample pairs for inversion training. The time-series sample construction module is used to standardize the amplitude values ​​in the sample pairs using Z-score and construct time-series training samples using a sliding time window. The model building and training module is used to construct a time-series inversion network based on the gated recurrent unit (GRU). It is trained using time-series training samples. During the training process, the learning rate of the time-series inversion network is adaptively optimized using the hybrid strategy whale optimization algorithm (HSWOA) to obtain the trained inversion model. and The inversion output module is used to input the amplitude time series of the actual observation data processed by the data acquisition and preprocessing module into the trained inversion model, and output the low ionosphere WS parameters to achieve inversion.

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